Calvin Ku September 27, 2016
Problem with trading is that you never know when is the best time to buy or sell a stock, as you never know if the stock price will go up or go down in the future. This simple trading bot is an attempt to solve this problem.
Given the historical data of a stock, our chimp will tell you whether you should buy or sell or hold a particular stock today (in our case, the JPM).
The only data used in this project is the JPM historical data collected from Yahoo Finance. The data ranges from December 30, 1983 to September 27, 2016. We don't use S&P 500 ETF as ETFs are generally arbitrageable which can render the techniques we will use in this project (namely, VPA) useless.
This project is about building a trading robot. In this proejct we will call it the Chimp. The Chimp is built to give the common user suggestions on whether to buy or sell or hold a particular stock on a particular trading day. The goal of this project is to build a trading robot that can beat a random monkey bot. Inpired by the famous saying of Princeton University professor Burton Malkiel in 1973 that "A blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by experts” and the Forbes article Any Monkey Can Beat the Market, instead of competing on a portfolio basis, we set our battlefield on JPM.
We will use JPM as an example in this project but the same method can be applied to any stock. In the end we will evaluate our method by giving the monkey bot (which chooses the three actions equally on a random basis) and our Chimp 1000 dollars and see how they perform from September 26, 2011 to September 27, 2016 on JPM.
In this project we use the cash in hand plus the portfolio value (number of shares in hand times the market price), the total assets as the metric. We also and define the reward function to be the ratio of the difference of the assets divided by the previous assets between the current state and the previous, i.e.: $$ R(s_i) = \frac{Cash(s_{i + 1}) + PV(s_{i + 1}) - Cash(s_i) - PV(s_i)}{Cash(s_i) + PV(s_i)} $$
This simple metric is in line with what we want the trading bot to achieve in that our ultimate goal is to make as much profit as possible given what we have put into the market, and it doesn't matter whether it's in cash or in shares.
In [57]:
from __future__ import division
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
from IPython.display import display
import pandas as pd
import numpy as np
from datetime import datetime, timedelta
import time
import random
from collections import defaultdict
from sklearn.ensemble import RandomForestRegressor
from copy import copy, deepcopy
from numba import jit
pd.set_option('display.max_columns', 50)
dfSPY = pd.read_csv('allSPY.csv', index_col='Date', parse_dates=True, na_values = ['nan'])
dfJPM = pd.read_csv('JPM.csv', index_col='Date', parse_dates=True, na_values = ['nan'])
# del dfSPY.index.name
del dfJPM.index.name
# display(dfSPY)
start_date = '1983-12-30'
end_date = '2016-09-27'
dates = pd.date_range(start_date, end_date)
dfMain = pd.DataFrame(index=dates)
# dfMain = dfMain.join(dfSPY)
dfMain = dfMain.join(dfJPM)
dfMain.dropna(inplace=True)
print("Start date: {}".format(dfMain.index[0]))
print("End date: {}\n".format(dfMain.index[-1]))
print(dfMain.describe())
Start date: 1983-12-30 00:00:00
End date: 2016-09-27 00:00:00
Open High Low Close Volume \
count 8256.000000 8256.000000 8256.000000 8256.000000 8.256000e+03
mean 46.472522 47.047441 45.882564 46.475389 1.290023e+07
std 20.463781 20.687878 20.250667 20.470789 1.835588e+07
min 10.250010 10.875000 9.624990 10.125000 3.780000e+04
25% 35.124990 35.527499 34.625010 35.060001 1.882275e+06
50% 41.000010 41.500000 40.500000 40.965000 7.037000e+06
75% 52.612501 53.092500 52.000000 52.542501 1.529572e+07
max 147.000000 149.124985 144.000000 147.000000 2.172942e+08
Adj Close
count 8256.000000
mean 22.914243
std 17.191570
min 1.514014
25% 5.380651
50% 23.981890
75% 33.764691
max 68.076434
In [58]:
print("\nInspect missing values:")
display(dfMain.isnull().sum())
Inspect missing values:
Open 0
High 0
Low 0
Close 0
Volume 0
Adj Close 0
dtype: int64
Since we won't be using data prior to 1993 for training, we can use SPY (S&P 500 ETF) to get trading days and see if we have any data missing for JPM.
In [61]:
spy_dates = pd.date_range('1993-01-29', end_date)
dfSPY = dfSPY.ix[spy_dates, :]
dfSPY.dropna(inplace=True)
print("Number of trading days: {}".format(len(dfSPY)))
print("Number of days where JPM are traded: {}".format(len(dfMain.ix[dfSPY.index, :])))
Number of trading days: 5960
Number of days where JPM are traded: 5960
It seems to be good. Let's look at the first few lines:
In [3]:
display(dfMain.head())
Open
High
Low
Close
Volume
Adj Close
1983-12-30
44.000008
44.500006
43.500014
44.000008
211500.0
2.602623
1984-01-03
43.937506
44.249986
43.624979
44.000008
385500.0
2.602623
1984-01-04
44.843758
45.874979
44.249986
45.874979
292500.0
2.713529
1984-01-05
46.812508
47.375008
46.250008
47.375008
344100.0
2.802256
1984-01-06
46.875014
47.375008
46.375021
46.875014
194400.0
2.772681
We can see that we have six columns: Open, High, Low, Close, Volume, Adj Close. The Adj Close is the closing price of that day adjusted for "future" dividends payout and splits. For our usage, we will need to adjust the rest of columns as well.
In [4]:
dfMain['Adj Close'].plot(figsize=(14, 7))
Out[4]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f8c13357410>
Starting from the beginning, the stock price generally has a upward trend, with a bad time from 2001 to 2003 and the crush at the end of 2008.
Now we can take a look at the correlations between the variables:
In [5]:
g = sns.PairGrid(dfMain)
g.map_upper(plt.scatter, alpha=0.3)
g.map_lower(plt.scatter, alpha=0.3)
g.map_diag(sns.kdeplot, lw=3, legend=False)
plt.subplots_adjust(top=0.95)
g.fig.suptitle('Feature Pair Grid')
Out[5]:
<matplotlib.text.Text at 0x7f8c0d135ad0>
We can see it clearly on the Adj Close rows and columns there are several lines. This is due to the fact that the Adj Close varaible are adjusted for times where there are splits and dividends payout. From here we know we'll need to adjust other variables to match it.
The trading bot (from now on we refer to it as the Chimp, coined with our wishful expectation that she will be smarter than the Monkey Trader) consists of two parts. In the first part we implement Q-learning and run it through the historical data for some number of iterations to construct the Q-table. The Chimp can then go with the optimal policy by following the action of which the state-action pair has the maximum Q value. However, since the state space is vast and the coverage of the Q-table is very small, in the second part we use supervised learning to train on the Q-table and make predictions for the unseen states.
The core idea of reinforcement learning is simple.
One way to do this is to use a method called Q-learning. At the core of Q-learning is the Bellman equation.
In each iteration we use the Bellman equation to update the cell of our Q-table: $$ Q(s, a) \longleftarrow (1 - \alpha) \ Q(s, a) + \alpha \ (R(s) + \gamma \ max_{a'} Q(s', a')) $$
where (s, a) is the state-action pair, $\alpha$ the learning rate, $R(s)$ the reward function, and $\gamma$ the discount factor. And then the Chimp will follow the policy: $$ \pi(s) = argmax_{a}Q(s, a) $$
Although we don't have the Q value of any state-action pair to begin with, the reward function contains the "real" information and throughout the iterations that information will slowly propagate to each state-action pair. At some point the Q values will converge to a practical level (hopefully), and we end up with a Q table in psudo-equilibrium.
However, there's a catch. How does the Chimp know what to do before she has learned anything?
One important concept of reinforcement learning is the exploration-exploitation dilemma. Essentially it means when we take an action, we have to choose between whether to explore new possibilities, or just to follow what we've known to be best, to the best of our knowledge. And of course, if we don't know much, then following that limited knowledge of ours wouldn't make much sense. On the other hand, if we've already known pretty much everything, then there's just not much to explore, and wandering around mindlessly wouldn't make sense either.
To implement this concept, we want our Chimp to set out not having a bias (not that she's got much anyways), so we introduce the variable $\epsilon$, which represents the possibility of the Chimp taking random actions. Initially we set $\epsilon = 1$ , and gradually decreases its value as the Chimp getting to know more and more about its environment. As time goes, the Chimp will become wiser and wiser and spends most of her time following what's best for her, and less time on being an explorer.
For the supervised learning part, we will use the random forest. The random forest doesn't expect linear features or assuming features interacting with each other linearly. It has the advantage of a decision tree which generally can fit into any shape of data, while being ensemble and eliminates the problem of a decision tree being easily overfitting. The random and ensemble nature of the algorithm makes it very unlikely to overfit on the training data. Since we are combining supervised learning with reinforcement learning, the problem gets more complicated and we will have more parameters to tune, and it's good to have an algorithm that kind of works "out of the box" most of the time. On the other hand, random forest handles high dimensionality very well, which makes feature engineering a bit easier where we don't need to worry too much about whether it's the newly engineered features not representative or it's the algorithm not able to handle the enlarged dimensionality. In addition to this, random forest itself is very easy to tune. We can easily grid search through number of choices of features for each splitting and the number of trees. The ensemble nature of the algorithm also makes it scalable when we need to: 1. train on more data, 2. build more trees, 3. take more stocks into account . Overall, random forest generally gives good results and it has been recognized that ensemble algorithms like random forest perform over other traditional algorithms in the Kaggle community over the years and have become quite popular.
The random forest is an ensemble method, which "ensembles" a bunch of decision trees. Each decision tree is generated by creating "nodes" with features in our dataset.
In the training stage, a data point comes down and through the nodes of the decision tree. Each node classifies the data point and sends it to the next node. Say, for example we are classifying people to determine whether their annual income is above or below average, and one feature of our data is gender. And we will probably have values like male/female/other. Now say this data point is a female, then it will get sent down the path accordingly to the next node. The node at the bottom of the decision tree is sometimes referred to as a leaf. Our data point will end up in one of the leaves, and the label of the data point is going to mark that leaf. For example, if our data point is above income average, then we mark that leaf as "above count +1". At the end of the training, all leaves will be marked with labels above or below.
In the predicting stage, we run data down the decision tree and see which leaves they end up with. And then we assign the data the labels of the leaves accordingly.
We now know how each decision tree is constructed and have a forest of decision trees. The last step is to get these decision trees to vote. If 10 trees say this person is above and 5 say below, we predict the person as above.
As said earlier, the decision trees are constructed with the features of our dataset. However, not all of the features are used to construct each decision tree. This is where the random part of the algorithm comes in. Most implementation employs a method called bagging, which generates $m$ sub-datasets from the feature space of the orginal dataset by sampling with replacement, where the size of the sub-datasets is $n'$, relative to the size of the feature space of the original dataset, $n$. The features of each bag are then used to construct a decision tree model.
We won't cover everything about the random forest here. However it's worth noting some of the more important specifics of random forest that are not covered here:
We shall set three different benchmarks here. One theoretical, and two practical.
Since our goal is to make as much money as possible. The best role model we can have, would be a God Chimp. A God Chimp is a Chimp that can foresee the future, and trades accordingly. In our case, this is not very hard to do. We can instantiate a Chimp object and get her to iterate through the entire dataset, until the whole Q-table converges. And with that Q-table in hand, we can get the psudo-perfect action series, which can make us a good deal of money. We then compute the accuracy of the action series of our mortal Chimp for that of the God Chimp. Theoretically speaking, the higher the accuracy, the closer the behavior of the mortal Chimp to the God Chimp, the more money the mortal Chimp would be making.
That said, the ups and downs of the stock market are not really uniformly distributed. This means our mortal Chimp could have a very decent accuracy for the God Chimp, but say, screwed up most of the important part. And therefore not really doing that well. Conversely, it may appear that our mortal Chimp is doing really terrible mimicing the God Chimp, but still makes a lot of money. So we will need some practical benchmarks that are more down to earth.
We shall test our Chimp against 100,000 random Monkeys and the Patient Trader we have defined earlier. Since these two naive traders don't get influenced by the media or manipulated by the market makers, they are proven to perform better than the average investor. We are happy as long as our Chimp can perform better than the Monkey, which means our Chimp is at least better than chance (and therefore better than any average person), and also it'd be great if she can beat the PT. However beating the PT in general means beating the market, which isn't something really easy to do. So we wouldn't expect that much here.
In [6]:
display(dfMain.head())
Open
High
Low
Close
Volume
Adj Close
1983-12-30
44.000008
44.500006
43.500014
44.000008
211500.0
2.602623
1984-01-03
43.937506
44.249986
43.624979
44.000008
385500.0
2.602623
1984-01-04
44.843758
45.874979
44.249986
45.874979
292500.0
2.713529
1984-01-05
46.812508
47.375008
46.250008
47.375008
344100.0
2.802256
1984-01-06
46.875014
47.375008
46.375021
46.875014
194400.0
2.772681
As said earlier, we need to adjust the prices of Open, High, Low, Close, Volume. This can be done by getting the adjustment fact by dividing Adj Close by Close. We then multiply the prices by this factor, and divide the volume by this factor.
In [7]:
# Adjust Open, High, Low, Volume
dfMain['Adj Factor'] = dfMain['Adj Close'] / dfMain['Close']
dfMain['Open'] = dfMain['Open'] * dfMain['Adj Factor']
dfMain['High'] = dfMain['High'] * dfMain['Adj Factor']
dfMain['Low'] = dfMain['Low'] * dfMain['Adj Factor']
dfMain['Volume'] = dfMain['Volume'] / dfMain['Adj Factor']
dfMain.drop(['Adj Factor'], axis=1, inplace=True)
display(dfMain.head())
display(dfMain.tail())
Open
High
Low
Close
Volume
Adj Close
1983-12-30
2.602623
2.632198
2.573048
44.000008
3.575624e+06
2.602623
1984-01-03
2.598926
2.617409
2.580440
44.000008
6.517272e+06
2.602623
1984-01-04
2.652532
2.713529
2.617410
45.874979
4.945011e+06
2.713529
1984-01-05
2.768984
2.802256
2.735712
47.375008
5.817363e+06
2.802256
1984-01-06
2.772681
2.802256
2.743106
46.875014
3.286531e+06
2.772681
Open
High
Low
Close
Volume
Adj Close
2016-09-21
66.839996
67.129997
66.309998
66.839996
14116800.0
66.839996
2016-09-22
66.989998
67.419998
66.839996
67.389999
12781700.0
67.389999
2016-09-23
67.389999
67.900002
67.180000
67.250000
13967400.0
67.250000
2016-09-26
66.599998
66.800003
65.540001
65.779999
16408100.0
65.779999
2016-09-27
65.410004
66.410004
65.110001
66.360001
13580600.0
66.360001
Volume price analysis has been around for over 100 years, and there are many legendary traders who made themselves famous (and wealthy) using it. In addition to this, the basic principle behind it kind of makes sense on its own, that:
But then people, especially practioners, tend to think of it as an art rather than science, in that even though you have some clues what's going on on the market, you still don't know what the best timing is. And it takes practice and practice until you "get it".
For we data scientists, everything is science, including art. If a human can stare at the candlesticks telling you when to buy or sell, so can a computer. Thus the following features are extracted from the raw dataset:
For volume:
For price:
For wick:
where -nd represents n day in the past.
The reason why we choose 5, 10, 21, 63 days is because these are the common time ranges used in technical analysis, where 5 days correspond to one trading week, 10 to two, and 21 days correspond to one trading month, 63 to three. We don't want to explode our feature space so to start with we use the most recent 5-day data with longer term average data.
Spread and wicks are terms to describe the status of the candlestick chart (see below).
The spread describes the thick body part of the candlestick which shows the difference of the opening price and the closing price. The time frame (in terms of opening/closing) can range from minutes to months depending on what we want to look at (in our case, the time frame is one day). The wicks are the thin lines that extend at the top and the bottom, which describe whether there are stocks traded at prices beyond opening/closing prices during the day (or the specific time frame of interest). As shown in the picture, we can have white or black bodies on the candlestick chart to indicate the direction of the pricing movement, with white meaning $\text{closing price} > \text{opening price}$ and vice versa. On the other hand, a candle can have a upperwick and/or a lowerwick or none at all.
Note that to implement Q-learning we need to make the variables discrete. We use 100 day maximum and 100 day average to divide the above features and get relative levels of those features.
We set the trading price of each trading day to be the Adjusted Close: $$ Trade Price = Adj\ Close $$ This information is not available to the Chimp. The properties of the Chimp get updated with this information when she places an order. The portfolio value also gets updated using this price.
In [8]:
# Price Engineering
# Get opens
period_list = [1, 2, 3, 4, 5, 10, 21, 63, 100]
for x in period_list:
dfMain['-' + str(x) + 'd_Open'] = dfMain['Open'].shift(x)
# Get adjCloses
period_list = xrange(1, 5 + 1)
for x in period_list:
dfMain['-' + str(x) + 'd_adjClose'] = dfMain['Adj Close'].shift(x)
# Get highs
period_list1 = xrange(1, 5 + 1)
for x in period_list1:
dfMain['-' + str(x) + 'd_High'] = dfMain['High'].shift(x)
period_list2 = [10, 21, 63, 100]
for x in period_list2:
dfMain[str(x) + 'd_High'] = dfMain['High'].shift().rolling(window=x).max()
# Get lows
period_list1 = xrange(1, 5 + 1)
for x in period_list1:
dfMain['-' + str(x) + 'd_Low'] = dfMain['Low'].shift(x)
period_list2 = [10, 21, 63, 100]
for x in period_list2:
dfMain[str(x) + 'd_Low'] = dfMain['High'].shift().rolling(window=x).min()
In [9]:
# Get Volume Bases
dfMain['100d_Avg_Vol'] = dfMain['Volume'].shift().rolling(window=100).mean() * 1.5
dfMain['100d_Max_Vol'] = dfMain['Volume'].shift().rolling(window=100).max()
# Get Spread Bases
dfMain['Abs_Spread'] = np.abs(dfMain['Adj Close'] - dfMain['Open'])
dfMain['Abs_Spread_Shift1'] = dfMain['Abs_Spread'].shift()
dfMain['100d_Avg_Spread'] = dfMain['Abs_Spread_Shift1'].rolling(window=100).mean() * 1.5
dfMain['100d_Max_Spread'] = dfMain['100d_High'] - dfMain['100d_Low']
dfMain.drop(['Abs_Spread_Shift1', 'Abs_Spread'], axis=1, inplace=True)
display(dfMain.tail())
display(dfMain.ix[datetime(2011, 12, 30)][['Open', 'Adj Close']])
Open
High
Low
Close
Volume
Adj Close
-1d_Open
-2d_Open
-3d_Open
-4d_Open
-5d_Open
-10d_Open
-21d_Open
-63d_Open
-100d_Open
-1d_adjClose
-2d_adjClose
-3d_adjClose
-4d_adjClose
-5d_adjClose
-1d_High
-2d_High
-3d_High
-4d_High
-5d_High
10d_High
21d_High
63d_High
100d_High
-1d_Low
-2d_Low
-3d_Low
-4d_Low
-5d_Low
10d_Low
21d_Low
63d_Low
100d_Low
100d_Avg_Vol
100d_Max_Vol
100d_Avg_Spread
100d_Max_Spread
2016-09-21
66.839996
67.129997
66.309998
66.839996
14116800.0
66.839996
66.750000
66.150002
66.089996
66.290001
66.269997
67.160004
65.750000
62.463746
62.602664
66.459999
66.190002
65.820000
66.639999
66.400002
66.849998
66.639999
66.260002
66.930000
67.250000
67.680000
67.769997
67.769997
67.769997
66.239998
65.849998
65.440002
66.089996
66.209999
66.260002
65.879997
58.296187
58.296187
2.162303e+07
4.445207e+07
0.555336
9.473810
2016-09-22
66.989998
67.419998
66.839996
67.389999
12781700.0
67.389999
66.839996
66.750000
66.150002
66.089996
66.290001
67.220001
66.070000
63.207953
63.198027
66.839996
66.459999
66.190002
65.820000
66.639999
67.129997
66.849998
66.639999
66.260002
66.930000
67.680000
67.769997
67.769997
67.769997
66.309998
66.239998
65.849998
65.440002
66.089996
66.260002
66.139999
58.296187
58.296187
2.158722e+07
4.445207e+07
0.553699
9.473810
2016-09-23
67.389999
67.900002
67.180000
67.250000
13967400.0
67.250000
66.989998
66.839996
66.750000
66.150002
66.089996
67.029999
65.989998
60.012824
62.414134
67.389999
66.839996
66.459999
66.190002
65.820000
67.419998
67.129997
66.849998
66.639999
66.260002
67.430000
67.769997
67.769997
67.769997
66.839996
66.309998
66.239998
65.849998
65.440002
66.260002
66.139999
58.296187
58.296187
2.162404e+07
4.445207e+07
0.558211
9.473810
2016-09-26
66.599998
66.800003
65.540001
65.779999
16408100.0
65.779999
67.389999
66.989998
66.839996
66.750000
66.150002
66.139999
65.910004
58.256495
61.273014
67.250000
67.389999
66.839996
66.459999
66.190002
67.900002
67.419998
67.129997
66.849998
66.639999
67.900002
67.900002
67.900002
67.900002
67.180000
66.839996
66.309998
66.239998
65.849998
66.260002
66.139999
58.296187
58.296187
2.154451e+07
4.445207e+07
0.555250
9.603815
2016-09-27
65.410004
66.410004
65.110001
66.360001
13580600.0
66.360001
66.599998
67.389999
66.989998
66.839996
66.750000
66.110001
66.330002
58.732788
61.124170
65.779999
67.250000
67.389999
66.839996
66.459999
66.800003
67.900002
67.419998
67.129997
66.849998
67.900002
67.900002
67.900002
67.900002
65.540001
67.180000
66.839996
66.309998
66.239998
66.260002
66.260002
59.090007
58.296187
2.153319e+07
4.445207e+07
0.564871
9.603815
Open 29.013163
Adj Close 29.135839
Name: 2011-12-30 00:00:00, dtype: float64
In [10]:
@jit
def relative_transform(num):
if 0 <= num < 0.25:
return 1
elif 0.25 <= num < 0.5:
return 2
elif 0.5 <= num < 0.75:
return 3
elif 0.75 <= num < 1:
return 4
elif 1 <= num:
return 5
elif -0.25 <= num < 0:
return -1
elif -0.5 <= num < -0.25:
return -2
elif -0.75 <= num < -0.5:
return -3
elif -1 <= num < -0.75:
return -4
elif num < -1:
return -5
else:
num
# Volume Engineering
# Get volumes
period_list = xrange(1, 5 + 1)
for x in period_list:
dfMain['-' + str(x) + 'd_Vol'] = dfMain['Volume'].shift(x)
# Get avg. volumes
period_list = [10, 21, 63]
for x in period_list:
dfMain[str(x) + 'd_Avg_Vol'] = dfMain['Volume'].shift().rolling(window=x).mean()
# Get relative volumes 1
period_list = range(1, 5 + 1)
for x in period_list:
dfMain['-' + str(x) + 'd_Vol1'] = dfMain['-' + str(x) + 'd_Vol'] / dfMain['100d_Avg_Vol']
dfMain['-' + str(x) + 'd_Vol1'] = dfMain['-' + str(x) + 'd_Vol1'].apply(relative_transform)
# Get relative avg. volumes 1
period_list = [10, 21, 63]
for x in period_list:
dfMain[str(x) + 'd_Avg_Vol1'] = dfMain[str(x) + 'd_Avg_Vol'] / dfMain['100d_Avg_Vol']
dfMain[str(x) + 'd_Avg_Vol1'] = dfMain[str(x) + 'd_Avg_Vol1'].apply(relative_transform)
# Get relative volumes 2
period_list = xrange(1, 5 + 1)
for x in period_list:
dfMain['-' + str(x) + 'd_Vol2'] = dfMain['-' + str(x) + 'd_Vol'] / dfMain['100d_Max_Vol']
dfMain['-' + str(x) + 'd_Vol2'] = dfMain['-' + str(x) + 'd_Vol2'].apply(relative_transform)
In [11]:
# Spread Engineering
# Get spread
period_list1 = xrange(1, 5 + 1)
period_list2 = [10, 21, 63]
for x in period_list1:
dfMain['-' + str(x) + 'd_Spread'] = dfMain['-' + str(x) + 'd_adjClose'] - dfMain['-' + str(x) + 'd_Open']
for x in period_list2:
dfMain[str(x) + 'd_Spread'] = dfMain['-1d_adjClose'] - dfMain['-' + str(x) + 'd_Open']
# Get relative spread
period_list1 = xrange(1, 5 + 1)
period_list2 = [10, 21, 63]
for x in period_list1:
dfMain['-' + str(x) + 'd_Spread'] = dfMain['-' + str(x) + 'd_Spread'] / dfMain['100d_Avg_Spread']
dfMain['-' + str(x) + 'd_Spread'] = dfMain['-' + str(x) + 'd_Spread'].apply(relative_transform)
for x in period_list2:
dfMain[str(x) + 'd_Spread'] = dfMain[str(x) + 'd_Spread'] / dfMain['100d_Max_Spread']
dfMain[str(x) + 'd_Spread'] = dfMain[str(x) + 'd_Spread'].apply(relative_transform)
display(dfMain[['-1d_Spread', '-2d_Spread', '-3d_Spread', '-4d_Spread', '-5d_Spread', '21d_Spread']].tail())
-1d_Spread
-2d_Spread
-3d_Spread
-4d_Spread
-5d_Spread
21d_Spread
2016-09-21
-3.0
1.0
-2.0
3.0
1.0
1.0
2016-09-22
1.0
-3.0
1.0
-2.0
3.0
1.0
2016-09-23
3.0
1.0
-3.0
1.0
-2.0
1.0
2016-09-26
-2.0
3.0
1.0
-3.0
1.0
1.0
2016-09-27
-5.0
-1.0
3.0
1.0
-3.0
-1.0
In [12]:
# Get wicks
@jit
def upperwick(open, adj_close, high):
if high > open and high > adj_close:
return True
else:
return False
def lowerwick(open, adj_close, low):
if low < open and low < adj_close:
return True
else:
return False
start_time = time.time()
period_list1 = xrange(1, 5 + 1)
period_list2 = [10, 21, 63, 100]
for x in period_list1:
dfMain.ix[:, '-' + str(x) + 'd_upperwick_bool'] = dfMain.apply(lambda row: upperwick(row['-' + str(x) + 'd_Open'], row['-' + str(x) + 'd_adjClose'], row['-' + str(x) + 'd_High']), axis=1)
dfMain.ix[:, '-' + str(x) + 'd_lowerwick_bool'] = dfMain.apply(lambda row: lowerwick(row['-' + str(x) + 'd_Open'], row['-' + str(x) + 'd_adjClose'], row['-' + str(x) + 'd_Low']), axis=1)
for x in period_list2:
dfMain.ix[:, str(x) + 'd_upperwick_bool'] = dfMain.apply(lambda row: upperwick(row['-' + str(x) + 'd_Open'], row['-1d_adjClose'], row[str(x) + 'd_High']), axis=1)
dfMain.ix[:, str(x) + 'd_lowerwick_bool'] = dfMain.apply(lambda row: lowerwick(row['-' + str(x) + 'd_Open'], row['-1d_adjClose'], row[str(x) + 'd_Low']), axis=1)
print("Getting wicks took {} seconds.".format(time.time() - start_time))
Getting wicks took 8.72208499908 seconds.
In [13]:
@jit
def get_upperwick_length(open, adj_close, high):
return high - max(open, adj_close)
@jit
def get_lowerwick_length(open, adj_close, low):
return min(open, adj_close) - low
start_time = time.time()
# Transform upper wicks
period_list1 = xrange(1, 5 + 1)
period_list2 = [10, 21, 63]
for x in period_list1:
has_upperwicks = dfMain['-' + str(x) + 'd_upperwick_bool']
has_lowerwicks = dfMain['-' + str(x) + 'd_lowerwick_bool']
dfMain.loc[has_upperwicks, '-' + str(x) + 'd_upperwick'] = dfMain.loc[has_upperwicks, :].apply(lambda row: get_upperwick_length(row['-' + str(x) + 'd_Open'], row['-' + str(x) + 'd_adjClose'], row['-' + str(x) + 'd_High']), axis=1)
dfMain.loc[has_lowerwicks, '-' + str(x) + 'd_lowerwick'] = dfMain.loc[has_lowerwicks, :].apply(lambda row: get_lowerwick_length(row['-' + str(x) + 'd_Open'], row['-' + str(x) + 'd_adjClose'], row['-' + str(x) + 'd_Low']), axis=1)
# Get relative upperwick length
dfMain.loc[dfMain['-' + str(x) + 'd_upperwick_bool'], '-' + str(x) + 'd_upperwick'] = dfMain.loc[dfMain['-' + str(x) + 'd_upperwick_bool'], '-' + str(x) + 'd_upperwick'] / dfMain.loc[dfMain['-' + str(x) + 'd_upperwick_bool'], '100d_Avg_Spread']
# Get relative lowerwick length
dfMain.loc[dfMain['-' + str(x) + 'd_lowerwick_bool'], '-' + str(x) + 'd_lowerwick'] = dfMain.loc[dfMain['-' + str(x) + 'd_lowerwick_bool'], '-' + str(x) + 'd_lowerwick'] / dfMain.loc[dfMain['-' + str(x) + 'd_lowerwick_bool'], '100d_Avg_Spread']
# Transform upperwick ratio to int
dfMain.loc[dfMain['-' + str(x) + 'd_upperwick_bool'], '-' + str(x) + 'd_upperwick'] = dfMain.loc[dfMain['-' + str(x) + 'd_upperwick_bool'], '-' + str(x) + 'd_upperwick'].apply(relative_transform)
# Transform lowerwick ratio to int
dfMain.loc[dfMain['-' + str(x) + 'd_lowerwick_bool'], '-' + str(x) + 'd_lowerwick'] = dfMain.loc[dfMain['-' + str(x) + 'd_lowerwick_bool'], '-' + str(x) + 'd_lowerwick'].apply(relative_transform)
# Assign 0 to no-upperwick days
dfMain.loc[np.logical_not(dfMain['-' + str(x) + 'd_upperwick_bool']), '-' + str(x) + 'd_upperwick'] = 0
# Assign 0 to no-lowerwick days
dfMain.loc[np.logical_not(dfMain['-' + str(x) + 'd_lowerwick_bool']), '-' + str(x) + 'd_lowerwick'] = 0
for x in period_list2:
has_upperwicks = dfMain[str(x) + 'd_upperwick_bool']
has_lowerwicks = dfMain[str(x) + 'd_lowerwick_bool']
dfMain.loc[has_upperwicks, str(x) + 'd_upperwick'] = dfMain.loc[has_upperwicks, :].apply(lambda row: get_upperwick_length(row['-' + str(x) + 'd_Open'], row['-1d_adjClose'], row[str(x) + 'd_High']), axis=1)
dfMain.loc[has_lowerwicks, str(x) + 'd_lowerwick'] = dfMain.loc[has_lowerwicks, :].apply(lambda row: get_lowerwick_length(row['-' + str(x) + 'd_Open'], row['-1d_adjClose'], row[str(x) + 'd_Low']), axis=1)
# Get relative upperwick length
dfMain.loc[dfMain[str(x) + 'd_upperwick_bool'], str(x) + 'd_upperwick'] = dfMain.loc[dfMain[str(x) + 'd_upperwick_bool'], str(x) + 'd_upperwick'] / dfMain.loc[dfMain[str(x) + 'd_upperwick_bool'], '100d_Avg_Spread']
# Get relative lowerwick length
dfMain.loc[dfMain[str(x) + 'd_lowerwick_bool'], str(x) + 'd_lowerwick'] = dfMain.loc[dfMain[str(x) + 'd_lowerwick_bool'], str(x) + 'd_lowerwick'] / dfMain.loc[dfMain[str(x) + 'd_lowerwick_bool'], '100d_Avg_Spread']
# Transform upperwick ratio to int
dfMain.loc[dfMain[str(x) + 'd_upperwick_bool'], str(x) + 'd_upperwick'] = dfMain.loc[dfMain[str(x) + 'd_upperwick_bool'], str(x) + 'd_upperwick'].apply(relative_transform)
# Transform lowerwick ratio to int
dfMain.loc[dfMain[str(x) + 'd_lowerwick_bool'], str(x) + 'd_lowerwick'] = dfMain.loc[dfMain[str(x) + 'd_lowerwick_bool'], str(x) + 'd_lowerwick'].apply(relative_transform)
# Assign 0 to no-upperwick days
dfMain.loc[np.logical_not(dfMain[str(x) + 'd_upperwick_bool']), str(x) + 'd_upperwick'] = 0
# Assign 0 to no-lowerwick days
dfMain.loc[np.logical_not(dfMain[str(x) + 'd_lowerwick_bool']), str(x) + 'd_lowerwick'] = 0
print("Transforming wicks took {} seconds.".format(time.time() - start_time))
Transforming wicks took 7.03627705574 seconds.
In [14]:
display(dfMain[['-1d_lowerwick', '-2d_lowerwick', '-3d_lowerwick', '-4d_lowerwick', '-5d_lowerwick', '10d_lowerwick', '21d_lowerwick', '63d_lowerwick']].isnull().sum())
-1d_lowerwick 65
-2d_lowerwick 65
-3d_lowerwick 65
-4d_lowerwick 64
-5d_lowerwick 63
10d_lowerwick 30
21d_lowerwick 41
63d_lowerwick 27
dtype: int64
In [15]:
display(dfMain.head())
display(dfMain.tail())
Open
High
Low
Close
Volume
Adj Close
-1d_Open
-2d_Open
-3d_Open
-4d_Open
-5d_Open
-10d_Open
-21d_Open
-63d_Open
-100d_Open
-1d_adjClose
-2d_adjClose
-3d_adjClose
-4d_adjClose
-5d_adjClose
-1d_High
-2d_High
-3d_High
-4d_High
-5d_High
...
-5d_lowerwick_bool
10d_upperwick_bool
10d_lowerwick_bool
21d_upperwick_bool
21d_lowerwick_bool
63d_upperwick_bool
63d_lowerwick_bool
100d_upperwick_bool
100d_lowerwick_bool
-1d_upperwick
-1d_lowerwick
-2d_upperwick
-2d_lowerwick
-3d_upperwick
-3d_lowerwick
-4d_upperwick
-4d_lowerwick
-5d_upperwick
-5d_lowerwick
10d_upperwick
10d_lowerwick
21d_upperwick
21d_lowerwick
63d_upperwick
63d_lowerwick
1983-12-30
2.602623
2.632198
2.573048
44.000008
3.575624e+06
2.602623
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
...
False
False
False
False
False
False
False
False
False
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1984-01-03
2.598926
2.617409
2.580440
44.000008
6.517272e+06
2.602623
2.602623
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
2.602623
NaN
NaN
NaN
NaN
2.632198
NaN
NaN
NaN
NaN
...
False
False
False
False
False
False
False
False
False
NaN
NaN
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1984-01-04
2.652532
2.713529
2.617410
45.874979
4.945011e+06
2.713529
2.598926
2.602623
NaN
NaN
NaN
NaN
NaN
NaN
NaN
2.602623
2.602623
NaN
NaN
NaN
2.617409
2.632198
NaN
NaN
NaN
...
False
False
False
False
False
False
False
False
False
NaN
NaN
NaN
NaN
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1984-01-05
2.768984
2.802256
2.735712
47.375008
5.817363e+06
2.802256
2.652532
2.598926
2.602623
NaN
NaN
NaN
NaN
NaN
NaN
2.713529
2.602623
2.602623
NaN
NaN
2.713529
2.617409
2.632198
NaN
NaN
...
False
False
False
False
False
False
False
False
False
0.0
NaN
NaN
NaN
NaN
NaN
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1984-01-06
2.772681
2.802256
2.743106
46.875014
3.286531e+06
2.772681
2.768984
2.652532
2.598926
2.602623
NaN
NaN
NaN
NaN
NaN
2.802256
2.713529
2.602623
2.602623
NaN
2.802256
2.713529
2.617409
2.632198
NaN
...
False
False
False
False
False
False
False
False
False
0.0
NaN
0.0
NaN
NaN
NaN
NaN
NaN
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
5 rows × 105 columns
Open
High
Low
Close
Volume
Adj Close
-1d_Open
-2d_Open
-3d_Open
-4d_Open
-5d_Open
-10d_Open
-21d_Open
-63d_Open
-100d_Open
-1d_adjClose
-2d_adjClose
-3d_adjClose
-4d_adjClose
-5d_adjClose
-1d_High
-2d_High
-3d_High
-4d_High
-5d_High
...
-5d_lowerwick_bool
10d_upperwick_bool
10d_lowerwick_bool
21d_upperwick_bool
21d_lowerwick_bool
63d_upperwick_bool
63d_lowerwick_bool
100d_upperwick_bool
100d_lowerwick_bool
-1d_upperwick
-1d_lowerwick
-2d_upperwick
-2d_lowerwick
-3d_upperwick
-3d_lowerwick
-4d_upperwick
-4d_lowerwick
-5d_upperwick
-5d_lowerwick
10d_upperwick
10d_lowerwick
21d_upperwick
21d_lowerwick
63d_upperwick
63d_lowerwick
2016-09-21
66.839996
67.129997
66.309998
66.839996
14116800.0
66.839996
66.750000
66.150002
66.089996
66.290001
66.269997
67.160004
65.750000
62.463746
62.602664
66.459999
66.190002
65.820000
66.639999
66.400002
66.849998
66.639999
66.260002
66.930000
67.250000
...
True
True
True
True
False
True
True
True
True
1.0
2.0
4.0
3.0
2.0
3.0
3.0
2.0
5.0
1.0
4.0
2.0
5.0
0.0
5.0
5.0
2016-09-22
66.989998
67.419998
66.839996
67.389999
12781700.0
67.389999
66.839996
66.750000
66.150002
66.089996
66.290001
67.220001
66.070000
63.207953
63.198027
66.839996
66.459999
66.190002
65.820000
66.639999
67.129997
66.849998
66.639999
66.260002
66.930000
...
True
True
True
True
False
True
True
True
True
3.0
4.0
1.0
2.0
4.0
3.0
2.0
3.0
3.0
2.0
4.0
5.0
5.0
0.0
5.0
5.0
2016-09-23
67.389999
67.900002
67.180000
67.250000
13967400.0
67.250000
66.989998
66.839996
66.750000
66.150002
66.089996
67.029999
65.989998
60.012824
62.414134
67.389999
66.839996
66.459999
66.190002
65.820000
67.419998
67.129997
66.849998
66.639999
66.260002
...
True
True
True
True
False
True
True
True
True
1.0
2.0
3.0
4.0
1.0
2.0
4.0
3.0
2.0
3.0
1.0
5.0
3.0
0.0
3.0
5.0
2016-09-26
66.599998
66.800003
65.540001
65.779999
16408100.0
65.779999
67.389999
66.989998
66.839996
66.750000
66.150002
66.139999
65.910004
58.256495
61.273014
67.250000
67.389999
66.839996
66.459999
66.190002
67.900002
67.419998
67.129997
66.849998
66.639999
...
True
True
False
True
False
True
False
True
True
4.0
1.0
1.0
2.0
3.0
4.0
1.0
2.0
4.0
3.0
5.0
0.0
5.0
0.0
5.0
0.0
2016-09-27
65.410004
66.410004
65.110001
66.360001
13580600.0
66.360001
66.599998
67.389999
66.989998
66.839996
66.750000
66.110001
66.330002
58.732788
61.124170
65.779999
67.250000
67.389999
66.839996
66.459999
66.800003
67.900002
67.419998
67.129997
66.849998
...
True
True
False
True
False
True
False
True
True
2.0
2.0
4.0
1.0
1.0
2.0
3.0
4.0
1.0
2.0
5.0
0.0
5.0
0.0
5.0
0.0
5 rows × 105 columns
In [16]:
dfMain['Trade Price'] = dfMain['Adj Close']
print(dfMain[['Trade Price', 'Open', 'Adj Close']].head())
Trade Price Open Adj Close
1983-12-30 2.602623 2.602623 2.602623
1984-01-03 2.602623 2.598926 2.602623
1984-01-04 2.713529 2.652532 2.713529
1984-01-05 2.802256 2.768984 2.802256
1984-01-06 2.772681 2.772681 2.772681
In [17]:
display(dfMain.columns)
Index([u'Open', u'High', u'Low', u'Close', u'Volume', u'Adj Close',
u'-1d_Open', u'-2d_Open', u'-3d_Open', u'-4d_Open',
...
u'-4d_lowerwick', u'-5d_upperwick', u'-5d_lowerwick', u'10d_upperwick',
u'10d_lowerwick', u'21d_upperwick', u'21d_lowerwick', u'63d_upperwick',
u'63d_lowerwick', u'Trade Price'],
dtype='object', length=106)
In [18]:
dfMain.drop(['Open', 'High', 'Low', 'Close', 'Adj Close', 'Volume', \
'-1d_Vol', '-2d_Vol', '-3d_Vol', '-4d_Vol', '-5d_Vol', '10d_Avg_Vol', '21d_Avg_Vol', '63d_Avg_Vol', \
'-1d_Open', '-2d_Open', '-3d_Open', '-4d_Open', '-5d_Open', '-10d_Open', '-21d_Open', '-63d_Open', '-100d_Open', \
'-1d_adjClose', '-2d_adjClose', '-3d_adjClose', '-4d_adjClose', '-5d_adjClose', \
'-1d_High', '-2d_High', '-3d_High', '-4d_High', '-5d_High', '10d_High', '21d_High', '63d_High', '100d_High', \
'-1d_Low', '-2d_Low', '-3d_Low', '-4d_Low', '-5d_Low', '10d_Low', '21d_Low', '63d_Low', '100d_Low', \
'100d_Avg_Vol', '100d_Max_Vol', '100d_Avg_Spread', '100d_Max_Spread', \
'-1d_upperwick_bool', '-2d_upperwick_bool', '-3d_upperwick_bool', '-4d_upperwick_bool', '-5d_upperwick_bool', '10d_upperwick_bool', '21d_upperwick_bool', '63d_upperwick_bool', '100d_upperwick_bool', \
'-1d_lowerwick_bool', '-2d_lowerwick_bool', '-3d_lowerwick_bool', '-4d_lowerwick_bool', '-5d_lowerwick_bool', '10d_lowerwick_bool', '21d_lowerwick_bool', '63d_lowerwick_bool', '100d_lowerwick_bool'], \
axis=1, inplace=True)
In [19]:
display(dfMain.columns)
dfMain.dropna(inplace=True)
len(dfMain.columns)
Index([u'-1d_Vol1', u'-2d_Vol1', u'-3d_Vol1', u'-4d_Vol1', u'-5d_Vol1',
u'10d_Avg_Vol1', u'21d_Avg_Vol1', u'63d_Avg_Vol1', u'-1d_Vol2',
u'-2d_Vol2', u'-3d_Vol2', u'-4d_Vol2', u'-5d_Vol2', u'-1d_Spread',
u'-2d_Spread', u'-3d_Spread', u'-4d_Spread', u'-5d_Spread',
u'10d_Spread', u'21d_Spread', u'63d_Spread', u'-1d_upperwick',
u'-1d_lowerwick', u'-2d_upperwick', u'-2d_lowerwick', u'-3d_upperwick',
u'-3d_lowerwick', u'-4d_upperwick', u'-4d_lowerwick', u'-5d_upperwick',
u'-5d_lowerwick', u'10d_upperwick', u'10d_lowerwick', u'21d_upperwick',
u'21d_lowerwick', u'63d_upperwick', u'63d_lowerwick', u'Trade Price'],
dtype='object')
Out[19]:
38
In [22]:
data_full = copy(dfMain)
In [23]:
display(data_full.head())
display(data_full.tail())
-1d_Vol1
-2d_Vol1
-3d_Vol1
-4d_Vol1
-5d_Vol1
10d_Avg_Vol1
21d_Avg_Vol1
63d_Avg_Vol1
-1d_Vol2
-2d_Vol2
-3d_Vol2
-4d_Vol2
-5d_Vol2
-1d_Spread
-2d_Spread
-3d_Spread
-4d_Spread
-5d_Spread
10d_Spread
21d_Spread
63d_Spread
-1d_upperwick
-1d_lowerwick
-2d_upperwick
-2d_lowerwick
-3d_upperwick
-3d_lowerwick
-4d_upperwick
-4d_lowerwick
-5d_upperwick
-5d_lowerwick
10d_upperwick
10d_lowerwick
21d_upperwick
21d_lowerwick
63d_upperwick
63d_lowerwick
Trade Price
1984-05-23
1.0
5.0
1.0
2.0
1.0
2.0
2.0
3.0
1.0
2.0
1.0
1.0
1.0
-5.0
-5.0
4.0
-4.0
-2.0
-4.0
-2.0
-3.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
0.0
3.0
0.0
0.0
5.0
0.0
5.0
0.0
2.474736
1984-05-24
2.0
1.0
5.0
1.0
2.0
2.0
2.0
3.0
1.0
1.0
2.0
1.0
1.0
-5.0
-5.0
-5.0
4.0
-4.0
-4.0
-3.0
-4.0
4.0
0.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
4.0
0.0
5.0
0.0
5.0
0.0
2.497335
1984-05-25
5.0
2.0
1.0
5.0
1.0
5.0
3.0
3.0
5.0
1.0
1.0
1.0
1.0
-3.0
-5.0
-5.0
-5.0
4.0
-3.0
-3.0
-4.0
5.0
2.0
4.0
0.0
3.0
5.0
0.0
0.0
2.0
0.0
4.0
0.0
5.0
0.0
5.0
0.0
2.486037
1984-05-29
2.0
5.0
2.0
1.0
5.0
5.0
3.0
3.0
1.0
5.0
1.0
1.0
1.0
-2.0
-3.0
-5.0
-5.0
-5.0
-2.0
-3.0
-3.0
4.0
4.0
5.0
2.0
4.0
0.0
3.0
5.0
0.0
0.0
5.0
0.0
5.0
0.0
5.0
0.0
2.395634
1984-05-30
2.0
2.0
5.0
2.0
1.0
5.0
3.0
3.0
1.0
1.0
5.0
1.0
1.0
-5.0
-2.0
-3.0
-5.0
-5.0
-2.0
-4.0
-4.0
2.0
5.0
4.0
4.0
5.0
2.0
4.0
0.0
3.0
5.0
5.0
0.0
5.0
0.0
5.0
0.0
2.271333
-1d_Vol1
-2d_Vol1
-3d_Vol1
-4d_Vol1
-5d_Vol1
10d_Avg_Vol1
21d_Avg_Vol1
63d_Avg_Vol1
-1d_Vol2
-2d_Vol2
-3d_Vol2
-4d_Vol2
-5d_Vol2
-1d_Spread
-2d_Spread
-3d_Spread
-4d_Spread
-5d_Spread
10d_Spread
21d_Spread
63d_Spread
-1d_upperwick
-1d_lowerwick
-2d_upperwick
-2d_lowerwick
-3d_upperwick
-3d_lowerwick
-4d_upperwick
-4d_lowerwick
-5d_upperwick
-5d_lowerwick
10d_upperwick
10d_lowerwick
21d_upperwick
21d_lowerwick
63d_upperwick
63d_lowerwick
Trade Price
2016-09-21
2.0
3.0
5.0
3.0
3.0
3.0
3.0
3.0
1.0
2.0
3.0
2.0
2.0
-3.0
1.0
-2.0
3.0
1.0
-1.0
1.0
2.0
1.0
2.0
4.0
3.0
2.0
3.0
3.0
2.0
5.0
1.0
4.0
2.0
5.0
0.0
5.0
5.0
66.839996
2016-09-22
3.0
2.0
3.0
5.0
3.0
3.0
3.0
3.0
2.0
1.0
2.0
3.0
2.0
1.0
-3.0
1.0
-2.0
3.0
-1.0
1.0
2.0
3.0
4.0
1.0
2.0
4.0
3.0
2.0
3.0
3.0
2.0
4.0
5.0
5.0
0.0
5.0
5.0
67.389999
2016-09-23
3.0
3.0
2.0
3.0
5.0
3.0
3.0
3.0
2.0
2.0
1.0
2.0
3.0
3.0
1.0
-3.0
1.0
-2.0
1.0
1.0
4.0
1.0
2.0
3.0
4.0
1.0
2.0
4.0
3.0
2.0
3.0
1.0
5.0
3.0
0.0
3.0
5.0
67.250000
2016-09-26
3.0
3.0
3.0
2.0
3.0
3.0
3.0
3.0
2.0
2.0
2.0
1.0
2.0
-2.0
3.0
1.0
-3.0
1.0
1.0
1.0
4.0
4.0
1.0
1.0
2.0
3.0
4.0
1.0
2.0
4.0
3.0
5.0
0.0
5.0
0.0
5.0
0.0
65.779999
2016-09-27
4.0
3.0
3.0
3.0
2.0
3.0
3.0
3.0
2.0
2.0
2.0
2.0
1.0
-5.0
-1.0
3.0
1.0
-3.0
-1.0
-1.0
3.0
2.0
2.0
4.0
1.0
1.0
2.0
3.0
4.0
1.0
2.0
5.0
0.0
5.0
0.0
5.0
0.0
66.360001
The problem with time series data in contrast to cross-sectional ones is that we cannot rely on conventional methods such as cross-validation or the usual 4:3:3 train-cv-test testing framework, as all of these methods are based on the assumption that all our data are drawn from the same population and a careful selection of a sample (samples) with proper modelling can say a lot about the entire population (and of course, about the other carefully drawn samples). However, we are not so lucky when it comes to dealing with time series data, mostly because:
Most if not all of the time our model really isn't the underlying model, that is, the data doesn't really come from the model we use. So it works only for really limited range of time and as the time series gets longer the difference between our model on the training set and the underlying model starts to show.
Essentially the system we are looking at is a time-dependent one so the underlying model itself most likely changes from time to time (unless we're talking about some grand unified model that can model the whole universe), in which case, assuming one model structure will work on the entire period of data is just wishful thinking.
That said, a lot of time we wish that in the process of our research, we can find some "invariants" (or least psudo-invariants) in our data that doesn't change as time goes. Still, we don't know if they are out there or not.
As said above, we will thus employ a training-testing framework that rolls as time goes. In our case, we keep 35 trading months of data for training (how this is determined will be shown later), and use the model to predict for 7 days, and since we are probably more interested in the performance of the JPM of the recent years we will proceed as following:
We start off setting our parameters as follows:
iter_number = 5000Trading price—as mentioned earlier, we assume the trading price to be the same as the Adjusted Close.
No transaction cost—this can simplify the problem so that we can focus on modelling.
Two actions—we limit ourselves to only two actions, buy and sell. Again since there's no transaction cost, buying when there's no cash is equivalent to hold (and similar for the sell case). By limiting the size of the action space it's easier for our Q value to converge.
As mentioned above, we will use a roll-forward training framework to build our Chimp. We will first give it a few tries and fine-tune our parameters on the validation dataset. We shall call this the validation phase. And then we'll move on the to test on the test dataset, which will be referred to as the test phase.
We will set up our two benchmarks for the two phases for comparison. To recap, which include:
In [24]:
validation_start_date = datetime(2006, 9, 25)
validation_end_date = datetime(2011, 9, 27)
test_start_date = datetime(2011, 9, 26)
test_end_date = datetime(2016, 9, 27)
print("Validation phase")
print("{0} Trade Price: {1}".format(validation_start_date, data_full.ix[validation_start_date, 'Trade Price']))
print("{0} Trade Price: {1}".format(validation_end_date, data_full.ix[validation_end_date, 'Trade Price']))
validation_phase_data = data_full.ix[validation_start_date:validation_end_date, :]
print("Number of dates in validation dataset: {}\n".format(len(validation_phase_data)))
print("Test phase")
print("{0} Trade Price: {1}".format(test_start_date, data_full.ix[test_start_date, 'Trade Price']))
print("{0} Trade Price: {1}".format(test_end_date, data_full.ix[test_end_date, 'Trade Price']))
test_phase_data = data_full.ix[test_start_date:test_end_date, :]
print("Number of dates in test dataset: {}".format(len(test_phase_data)))
Validation phase
2006-09-25 00:00:00 Trade Price: 36.610129
2011-09-27 00:00:00 Trade Price: 27.422319
Number of dates in validation dataset: 1262
Test phase
2011-09-26 00:00:00 Trade Price: 27.491809
2016-09-27 00:00:00 Trade Price: 66.360001
Number of dates in test dataset: 1260
$Cash_{init} = 1000.00$
$Share_{init} = 0$
$PV_{init} = 0$
$Trading \ Price_{init} = 36.61$
$Share_{start} = floor(\frac{1000.00}{36.61}) = 27$
$PV_{start} = 36.61 \cdot 27 = 988.47$
$Cash_{start} = Cash_{init} - PV_{start} = 1000.00 - 988.47 = 11.53$
$Total \ Assets_{start} = Cash_{start} + PV_{start} = 1000.00$
$Cash_{end} = 11.53$ $Share_{end} = 27$ $Trading \ Price_{end} = 27.42$
$PV_{end} = 27.42 \cdot 27 = 740.34$
$Total \ Assets_{end} = Cash_{end} + PV_{end} = 11.53 + 740.34 = 751.87$
We can calculate the annual ROI by solving the following equation for $r_{val}$: $$ (1 + r)^{1260/252} = 0.7519 $$
$$ \Longrightarrow \boxed{r_{val} = -0.05543464 \approx -5.54\%} $$Similarly, we will have $$ \boxed{r_{test} = 0.1912884 \approx 19.13\%} $$
We use a MonkeyBot class which will place one and only one order randomly everyday. We iterate it through the time frame we choose 100,000 times and we get the following distributions:
In [25]:
import random
import time
from copy import deepcopy
class MonkeyBot(object):
def __init__(self, dfEnv, cash=1000, share=0, pv=0, now_yes_share=0, random_state=0):
random.seed(random_state)
self.cash = cash
self.share = share
self.pv = pv
self.pv_history_list = []
self.action_list = []
self.env = deepcopy(dfEnv)
def buy(self, stock_price):
num_affordable = int(self.cash // stock_price)
self.cash = self.cash - stock_price * num_affordable
self.share = self.share + num_affordable
self.pv = stock_price * self.share
self.action_list.append('Buy')
def sell(self, stock_price):
self.cash = self.cash + stock_price * self.share
self.pv = 0
self.share = 0
self.action_list.append('Sell')
def hold(self, stock_price):
self.pv = stock_price * self.share
self.action_list.append('Hold')
def reset(self):
self.cash = 1000
self.share = 0
self.pv = 0
def yes_share(self):
# Represent chimp asset in state_action
if self.share > 0:
return 1
else:
return 0
def make_decision(self, x):
random_choice = random.choice([1, 2])
if random_choice == 0:
self.hold(x)
elif random_choice == 1:
self.buy(x)
else:
self.sell(x)
return self.pv # for frame-wise operation
def simulate(self, iters):
for i in range(iters):
self.env['Monkey PV'] = self.env['Trade Price'].apply(self.make_decision)
self.pv_history_list.append(self.env.ix[-1, 'Monkey PV'] + self.cash)
self.reset()
In [26]:
monkey_val = MonkeyBot(validation_phase_data, random_state=0)
start_time = time.time()
iters = 100000
monkey_val.simulate(iters)
print("{0} iterations took {1} seconds".format(iters, time.time() - start_time))
100000 iterations took 297.804918051 seconds
In [27]:
plt.hist(monkey_val.pv_history_list, bins=50)
Out[27]:
(array([ 6.34800000e+03, 2.08350000e+04, 2.16270000e+04,
1.65640000e+04, 1.12580000e+04, 7.61500000e+03,
5.05600000e+03, 3.36200000e+03, 2.14800000e+03,
1.47100000e+03, 1.01100000e+03, 7.31000000e+02,
5.09000000e+02, 3.70000000e+02, 2.75000000e+02,
1.83000000e+02, 1.52000000e+02, 1.26000000e+02,
1.00000000e+02, 5.10000000e+01, 5.20000000e+01,
3.90000000e+01, 2.30000000e+01, 2.40000000e+01,
1.90000000e+01, 1.10000000e+01, 8.00000000e+00,
4.00000000e+00, 4.00000000e+00, 4.00000000e+00,
3.00000000e+00, 2.00000000e+00, 3.00000000e+00,
2.00000000e+00, 1.00000000e+00, 3.00000000e+00,
1.00000000e+00, 2.00000000e+00, 1.00000000e+00,
0.00000000e+00, 1.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
0.00000000e+00, 1.00000000e+00]),
array([ 85.447874 , 342.45150846, 599.45514292, 856.45877738,
1113.46241184, 1370.4660463 , 1627.46968076, 1884.47331522,
2141.47694968, 2398.48058414, 2655.4842186 , 2912.48785306,
3169.49148752, 3426.49512198, 3683.49875644, 3940.5023909 ,
4197.50602536, 4454.50965982, 4711.51329428, 4968.51692874,
5225.5205632 , 5482.52419766, 5739.52783212, 5996.53146658,
6253.53510104, 6510.5387355 , 6767.54236996, 7024.54600442,
7281.54963888, 7538.55327334, 7795.5569078 , 8052.56054226,
8309.56417672, 8566.56781118, 8823.57144564, 9080.5750801 ,
9337.57871456, 9594.58234902, 9851.58598348, 10108.58961794,
10365.5932524 , 10622.59688686, 10879.60052132, 11136.60415578,
11393.60779024, 11650.6114247 , 11907.61505916, 12164.61869362,
12421.62232808, 12678.62596254, 12935.629597 ]),
<a list of 50 Patch objects>)
In [28]:
monkey_val_stats = pd.Series(monkey_val.pv_history_list)
print(monkey_val_stats.describe())
count 100000.000000
mean 1060.238834
std 728.393854
min 85.447874
25% 575.907935
50% 872.079011
75% 1327.014578
max 12935.629597
dtype: float64
In [30]:
monkey_test = MonkeyBot(test_phase_data, random_state=0)
start_time = time.time()
iters = 100000
monkey_test.simulate(iters)
print("{0} iterations took {1} seconds".format(iters, time.time() - start_time))
100000 iterations took 276.959551096 seconds
In [31]:
plt.hist(monkey_test.pv_history_list, bins=50)
Out[31]:
(array([ 4.00000000e+00, 2.10000000e+01, 1.36000000e+02,
4.72000000e+02, 1.08800000e+03, 2.06900000e+03,
3.36000000e+03, 4.82700000e+03, 6.27800000e+03,
7.27500000e+03, 7.81400000e+03, 8.06700000e+03,
7.98500000e+03, 7.47900000e+03, 7.03600000e+03,
6.17200000e+03, 5.41600000e+03, 4.60700000e+03,
4.00500000e+03, 3.22600000e+03, 2.75700000e+03,
2.14500000e+03, 1.71600000e+03, 1.30400000e+03,
1.03900000e+03, 8.09000000e+02, 6.83000000e+02,
5.25000000e+02, 3.81000000e+02, 2.92000000e+02,
2.53000000e+02, 1.93000000e+02, 1.49000000e+02,
1.02000000e+02, 7.70000000e+01, 4.60000000e+01,
4.70000000e+01, 3.40000000e+01, 2.40000000e+01,
2.50000000e+01, 1.20000000e+01, 1.10000000e+01,
1.50000000e+01, 7.00000000e+00, 3.00000000e+00,
4.00000000e+00, 2.00000000e+00, 4.00000000e+00,
3.00000000e+00, 1.00000000e+00]),
array([ 422.648034 , 508.28394454, 593.91985508, 679.55576562,
765.19167616, 850.8275867 , 936.46349724, 1022.09940778,
1107.73531832, 1193.37122886, 1279.0071394 , 1364.64304994,
1450.27896048, 1535.91487102, 1621.55078156, 1707.1866921 ,
1792.82260264, 1878.45851318, 1964.09442372, 2049.73033426,
2135.3662448 , 2221.00215534, 2306.63806588, 2392.27397642,
2477.90988696, 2563.5457975 , 2649.18170804, 2734.81761858,
2820.45352912, 2906.08943966, 2991.7253502 , 3077.36126074,
3162.99717128, 3248.63308182, 3334.26899236, 3419.9049029 ,
3505.54081344, 3591.17672398, 3676.81263452, 3762.44854506,
3848.0844556 , 3933.72036614, 4019.35627668, 4104.99218722,
4190.62809776, 4276.2640083 , 4361.89991884, 4447.53582938,
4533.17173992, 4618.80765046, 4704.443561 ]),
<a list of 50 Patch objects>)
In [32]:
monkey_test_stats = pd.Series(monkey_test.pv_history_list)
print(monkey_test_stats.describe())
count 100000.000000
mean 1606.960713
std 464.488921
min 422.648034
25% 1272.686842
50% 1542.634717
75% 1869.730139
max 4704.443561
dtype: float64
Using the mean we can calculate $r_{val}$: $$ (1 + r_{val})^{1260/252} = 0.8721 $$
$$ \Longrightarrow \boxed{r_{val} = -0.02699907 \approx -2.70\%} $$Similarly, $$ \Longrightarrow \boxed{r_{test} = 0.09056276 \approx 9.06\%} $$
In [33]:
from sklearn.ensemble import RandomForestRegressor
class ChimpBot(MonkeyBot):
"""A trading bot that learns to trade in the stock market."""
valid_actions = ['Buy', 'Sell']
epsilon = 1
gamma = 0.75
random_reward = [0]
random_counter = 0
policy_counter = 0
track_key1 = {'Sell': 0, 'Buy': 0, 'Hold': 0}
track_key2 = {'Sell': 0, 'Buy': 0, 'Hold': 0}
track_random_decision = {'Sell': 0, 'Buy': 0, 'Hold': 0}
reset_counter = 0
def __init__(self, dfEnv, iter_random_rounds, test_mode=False, cash=1000, share=0, pv=0, random_state=0):
super(ChimpBot, self).__init__(dfEnv, iter_random_rounds, cash, share, pv)
random.seed(random_state)
np.random.seed(random_state)
# sets self.cash = 1000
# sets self.share = 0
# sets self.pv = 0
# sets self.pv_history_list = []
# sets self.env = dfEnv
# implements buy(self, stock_price)
# implements sell(self, stock_price)
# implements hold(self)
self.test_mode = test_mode
self.num_features = len(dfEnv.columns) - 1
self.random_rounds = iter_random_rounds # Number of rounds where the bot chooses to go monkey
self.iter_env = self.env.iterrows()
self.now_env_index, self.now_row = self.iter_env.next()
# self.now_yes_share = 0
self.now_action = ''
# self.now_q = 0
self.prev_cash = self.cash
self.prev_share = self.share
self.prev_pv = self.pv
self.q_df_columns = list(self.env.columns)
self.q_df_columns.pop()
self.q_df_columns.extend(['Action', 'Q Value'])
self.q_df = pd.DataFrame(columns=self.q_df_columns)
self.q_dict = defaultdict(lambda: (0, 0)) # element of q_dict is (state, act): (q_value, t)
# self.q_dict_analysis preserves the datetime data and is not used by the ChimpBot
self.q_dict_analysis = defaultdict(lambda: (0, 0))
self.negative_reward = 0
self.n_reward_hisotry = []
self.net_reward = 0
self.reset_counter = 0
def make_q_df(self):
result_dict = defaultdict(list)
for index, row in self.q_dict.iteritems():
for i in range(len(self.q_dict.keys()[0])):
column_name = 'col' + str(i + 1)
result_dict[column_name].append(index[i])
result_dict['Q'].append(self.q_dict[index][0])
self.q_df = pd.DataFrame(result_dict)
q_df_column_list = ['col' + str(x) for x in range(1, self.num_features + 1 + 1)]
q_df_column_list.append('Q')
self.q_df = self.q_df[q_df_column_list]
def transfer_action(x):
if x == 'Buy':
return 1
elif x == 'Sell':
return 2
elif x == 'Hold':
return 0
else:
raise ValueError("Wrong action!")
def str_float_int(x):
return int(float(x))
arr_int = np.vectorize(str_float_int)
self.q_df['col' + str(self.num_features + 1)] = self.q_df['col' + str(self.num_features + 1)].apply(transfer_action)
self.q_df.ix[:, :-1] = self.q_df.ix[:, :-1].apply(arr_int)
def split_q_df(self):
self.q_df_X = self.q_df.ix[:, :-1]
self.q_df_y = self.q_df.ix[:, -1]
def train_on_q_df(self):
reg = RandomForestRegressor(n_estimators=128, max_features='sqrt', n_jobs=-1, random_state=0)
self.q_reg = reg
self.q_reg = self.q_reg.fit(self.q_df_X, self.q_df_y)
def update_q_model(self):
print("Updating Q model...")
start_time = time.time()
self.make_q_df()
self.split_q_df()
self.train_on_q_df()
def from_state_action_predict_q(self, state_action):
state_action = [state_action]
pred_q = self.q_reg.predict(state_action)
return pred_q
def max_q(self, now_row):
def transfer_action(x):
if x == 'Buy':
return 1
elif x == 'Sell':
return 2
elif x == 'Hold':
return 0
else:
raise ValueError("Wrong action!")
def str_float_int(x):
return int(float(x))
now_row2 = list(now_row)
# now_row2.append(self.now_yes_share)
max_q = ''
q_compare_dict = {}
if len(now_row2) > self.num_features:
raise ValueError("Got ya bastard! @ MaxQ")
# Populate the q_dict
for act in set(self.valid_actions):
now_row2.append(act)
now_row_key = tuple(now_row2)
_ = self.q_dict[now_row_key]
try:
self.q_reg
except AttributeError:
pass
# print('No q_reg yet...going with default.')
else:
if _[1] == 0:
single_X = np.array(now_row_key)
# print(single_X)
arr_int = np.vectorize(str_float_int)
single_X[-1] = transfer_action(single_X[-1])
single_X = arr_int(single_X)
single_X = single_X.reshape(1, -1)
pred_q = self.q_reg.predict(single_X)
dreamed_q = (1 - (1 / (self.q_dict[now_row_key][1] + 1))) * self.q_dict[now_row_key][0] + (1 / (self.q_dict[now_row_key][1] + 1)) * pred_q[0]
self.q_dict[now_row_key] = (dreamed_q, self.q_dict[now_row_key][1] + 1)
q_compare_dict[now_row_key] = self.q_dict[now_row_key]
now_row2.pop()
try:
max(q_compare_dict.iteritems(), key=lambda x:x[1])
except ValueError:
print("Wrong Q Value in Q Compare Dict!")
else:
key, qAndT = max(q_compare_dict.iteritems(), key=lambda x:x[1])
# print("Action: {0}, with Q-value: {1}".format(key[-1], qAndT[0]))
return key[-1], qAndT[0], qAndT[1]
def q_update(self):
# print("Data Index: {}".format(self.now_env_index))
now_states = list(self.now_row)
# now_states = list(now_states)
now_states.pop() # disregard the Trade Price
prev_states = list(self.prev_states)
if len(prev_states) > self.num_features:
raise ValueError("Got ya bastard! @ Q_Update...something wrong with the self.prev_states!!!")
# prev_states.append(self.prev_yes_share)
prev_states.append(self.prev_action)
prev_states_key = tuple(prev_states)
if len(prev_states_key) > self.num_features + 2:
raise ValueError("Got ya bastard! @ Q_Update")
q_temp = self.q_dict[prev_states_key]
q_temp0 = (1 - (1 / (q_temp[1] + 1))) * q_temp[0] + (1 / (q_temp[1] + 1)) * (self.reward + self.gamma * self.max_q(now_states)[1])
self.q_dict[prev_states_key] = (q_temp0, q_temp[1] + 1)
# For analysis purpose
self.q_dict_analysis[prev_states_key] = (q_temp0, self.prev_env_index)
# print("Now Action: {}".format())
# print(prev_states_key)
return (self.q_dict[prev_states_key])
def policy(self, now_row):
return self.max_q(now_row)[0]
def reset(self):
# Portfolio change over iterations
self.pv_history_list.append(self.pv + self.cash)
self.iter_env = self.env.iterrows()
self.now_env_index, self.now_row = self.iter_env.next()
self.cash = 1000
self.share = 0
self.pv = 0
self.prev_cash = self.cash
self.prev_share = self.share
self.prev_pv = self.pv
if self.test_mode is True:
self.epsilon = 0
else:
if self.epsilon - 1/self.random_rounds > 1/self.random_rounds: # Epislon threshold: 0.01
self.random_counter += 1
self.epsilon = self.epsilon - 1/self.random_rounds
else:
self.epsilon = 0.000001 # Epislon threshold: 0.1
self.policy_counter += 1
self.net_reward = 0
self.reset_counter += 1
if self.reset_counter % self.random_rounds == 0:
self.update_q_model()
if self.reset_counter != self.random_rounds:
self.action_list = []
def make_decision(self, now_row):
return self.policy(now_row)
def update(self):
# Update state
now_states = list(self.now_row)
if len(now_states) > self.num_features + 1:
print(len(now_states))
print(self.num_features)
raise ValueError("Got ya bastard! @ Q_Update...something wrong with the self.now_row!!!")
now_states.pop() # disregard the Trade Price
if len(now_states) > self.num_features:
print(now_states)
raise ValueError("Got ya bastard! @ Q_Update...something wrong with now_states after pop!!!")
# Exploitation-exploration decisioning
self.decision = np.random.choice(2, p = [self.epsilon, 1 - self.epsilon]) # decide to go random or with the policy
# self.decision = 0 # Force random mode
# print("Random decision: {0}, Epislon: {1}".format(self.decision, self.epsilon))
if self.decision == 0: # if zero, go random
action = random.choice(self.valid_actions)
else: # else go with the policy
action = self.make_decision(now_states)
if len(now_states) > self.num_features:
print(now_states)
raise ValueError("Got ya bastard! @ Q_Update...something wrong with now_states after make_decision!!!")
# Execute action and get reward
if action == 'Buy':
# print(self.now_row)
self.buy(self.now_row[-1])
elif action == 'Sell':
# print(self.now_row)
self.sell(self.now_row[-1])
elif action == 'Hold':
# print(self.now_row)
self.hold(self.now_row[-1])
else:
raise ValueError("Wrong action man!")
try:
self.prev_states
except AttributeError:
print("Running the first time...no prevs exist.")
else:
self.reward = ((self.cash - self.prev_cash) + (self.pv - self.prev_pv)) / (self.prev_cash + self.prev_pv)
self.q_update()
self.prev_states = now_states
if len(now_states) > self.num_features:
raise ValueError("Got ya bastard! @ Q_Update...something wrong with the now_states!!!")
self.now_action = action
self.prev_action = action
# self.prev_yes_share = self.now_yes_share
self.prev_env_index = deepcopy(self.now_env_index)
self.prev_cash = self.cash
self.prev_share = self.share
self.prev_pv = self.pv
try:
self.now_env_index, self.now_row = self.iter_env.next()
except StopIteration:
pass
# print("End of data.")
else:
pass
try:
_ = self.reward
except AttributeError:
print("No reward yet...0 assigned.")
self.reward = 0
def simulate(self):
start_time = time.time()
for i in range(self.random_rounds):
for l in range(len(self.env)):
self.update()
self.reset()
print("{0} rounds of simulation took {1} seconds".format(self.random_rounds, time.time() - start_time))
return self.pv_history_list
In [1038]:
iter_random_rounds=5000
god_chimp = ChimpBot(dfEnv=data_full, iter_random_rounds=iter_random_rounds, random_state=0)
pv_history_list = god_chimp.simulate()
print(pv_history_list[-1])
pd.Series(pv_history_list).plot()
Running the first time...no prevs exist.
No reward yet...0 assigned.
5000 rounds of simulation took 9646.88984394 seconds
2.05413123456e+31
Out[1038]:
<matplotlib.axes._subplots.AxesSubplot at 0x7fb7a8d09390>
In [1040]:
print(pd.Series(god_chimp.action_list).describe())
count 8156
unique 2
top Buy
freq 4123
dtype: object
In [1041]:
# Convert Q-Table to Dataframe from the God Chimp (full dataset)
iter_random_rounds=5000
result_dict = defaultdict(list)
for index, row in god_chimp.q_dict_analysis.iteritems():
for i in range(len(god_chimp.q_dict_analysis.keys()[0])):
column_name = 'col' + str(i + 1)
result_dict[column_name].append(index[i])
result_dict['Q'].append(god_chimp.q_dict_analysis[index][0])
result_dict['Date'].append(god_chimp.q_dict_analysis[index][1])
god_chimp_q_df = pd.DataFrame(result_dict)
# Yes share column removed
column_list = ['col1', 'col2', 'col3', 'col4', 'col5', 'col6', 'col7', 'col8', 'col9', 'col10', 'col11', 'col12', 'col13', 'col14', 'col15', 'col16', 'col17', 'col18', 'col19', 'col20', 'col21', 'col22', 'col23', 'col24', 'col25', 'col26', 'col27', 'col28', 'col29', 'col30', 'col31', 'col32', 'col33', 'col34', 'col35', 'col36', 'col37', 'col38', 'Date', 'Q']
god_chimp_q_df = god_chimp_q_df[column_list]
god_chimp_q_df.sort_values('Date', inplace=True)
god_chimp_q_df.reset_index(inplace=True)
del god_chimp_q_df['index']
god_chimp_q_df.reset_index(inplace=True)
del god_chimp_q_df['index']
god_chimp_q_df.set_index(god_chimp_q_df['Date'], inplace=True)
del god_chimp_q_df.index.name
del god_chimp_q_df['Date']
print(len(god_chimp_q_df))
display(god_chimp_q_df.head())
16312
col1
col2
col3
col4
col5
col6
col7
col8
col9
col10
col11
col12
col13
col14
col15
col16
col17
col18
col19
col20
col21
col22
col23
col24
col25
col26
col27
col28
col29
col30
col31
col32
col33
col34
col35
col36
col37
col38
Q
1984-05-23
1.0
5.0
1.0
2.0
1.0
2.0
2.0
3.0
1.0
2.0
1.0
1.0
1.0
-5.0
-5.0
4.0
-4.0
-2.0
-4.0
-2.0
-3.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
0.0
3.0
0.0
0.0
5.0
0.0
5.0
0.0
Sell
0.008839
1984-05-23
1.0
5.0
1.0
2.0
1.0
2.0
2.0
3.0
1.0
2.0
1.0
1.0
1.0
-5.0
-5.0
4.0
-4.0
-2.0
-4.0
-2.0
-3.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
0.0
3.0
0.0
0.0
5.0
0.0
5.0
0.0
Buy
0.019101
1984-05-24
2.0
1.0
5.0
1.0
2.0
2.0
2.0
3.0
1.0
1.0
2.0
1.0
1.0
-5.0
-5.0
-5.0
4.0
-4.0
-4.0
-3.0
-4.0
4.0
0.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
4.0
0.0
5.0
0.0
5.0
0.0
Sell
0.015100
1984-05-24
2.0
1.0
5.0
1.0
2.0
2.0
2.0
3.0
1.0
1.0
2.0
1.0
1.0
-5.0
-5.0
-5.0
4.0
-4.0
-4.0
-3.0
-4.0
4.0
0.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
4.0
0.0
5.0
0.0
5.0
0.0
Buy
0.009537
1984-05-25
5.0
2.0
1.0
5.0
1.0
5.0
3.0
3.0
5.0
1.0
1.0
1.0
1.0
-3.0
-5.0
-5.0
-5.0
4.0
-3.0
-3.0
-4.0
5.0
2.0
4.0
0.0
3.0
5.0
0.0
0.0
2.0
0.0
4.0
0.0
5.0
0.0
5.0
0.0
Buy
-0.015552
In [10]:
def action_to_int(string):
if string == 'Buy':
return 1
elif string == 'Sell':
return 2
else:
return string
god_chimp_q_df.ix[:, -2] = god_chimp_q_df.ix[:, -2].apply(action_to_int)
In [1044]:
god_chimp_q_df.head()
Out[1044]:
col1
col2
col3
col4
col5
col6
col7
col8
col9
col10
col11
col12
col13
col14
col15
col16
col17
col18
col19
col20
col21
col22
col23
col24
col25
col26
col27
col28
col29
col30
col31
col32
col33
col34
col35
col36
col37
col38
Q
1984-05-23
1.0
5.0
1.0
2.0
1.0
2.0
2.0
3.0
1.0
2.0
1.0
1.0
1.0
-5.0
-5.0
4.0
-4.0
-2.0
-4.0
-2.0
-3.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
0.0
3.0
0.0
0.0
5.0
0.0
5.0
0.0
2
0.008839
1984-05-23
1.0
5.0
1.0
2.0
1.0
2.0
2.0
3.0
1.0
2.0
1.0
1.0
1.0
-5.0
-5.0
4.0
-4.0
-2.0
-4.0
-2.0
-3.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
0.0
3.0
0.0
0.0
5.0
0.0
5.0
0.0
1
0.019101
1984-05-24
2.0
1.0
5.0
1.0
2.0
2.0
2.0
3.0
1.0
1.0
2.0
1.0
1.0
-5.0
-5.0
-5.0
4.0
-4.0
-4.0
-3.0
-4.0
4.0
0.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
4.0
0.0
5.0
0.0
5.0
0.0
2
0.015100
1984-05-24
2.0
1.0
5.0
1.0
2.0
2.0
2.0
3.0
1.0
1.0
2.0
1.0
1.0
-5.0
-5.0
-5.0
4.0
-4.0
-4.0
-3.0
-4.0
4.0
0.0
3.0
5.0
0.0
0.0
2.0
0.0
2.0
2.0
4.0
0.0
5.0
0.0
5.0
0.0
1
0.009537
1984-05-25
5.0
2.0
1.0
5.0
1.0
5.0
3.0
3.0
5.0
1.0
1.0
1.0
1.0
-3.0
-5.0
-5.0
-5.0
4.0
-3.0
-3.0
-4.0
5.0
2.0
4.0
0.0
3.0
5.0
0.0
0.0
2.0
0.0
4.0
0.0
5.0
0.0
5.0
0.0
1
-0.015552
As said earlier, one problem with time series data is to find the training window size wihtin which the data can be seen as being drawn from the same population as the data we want to predict. Then of course we can generalize what we have learned/modelled from the training to the cross-validation/test dataset.
To do this we can make use of the God Chimp’s Q-table we just got and get:
In [76]:
from sklearn.metrics import accuracy_score
def find_best_training_size(data_full, full_q_df, training_sizes, testing_size, target_data, random_state=0):
start_time = time.time()
accs = []
d_counter = 0
# Loop through all batches in validation dataset
(u, ) = data_full.index.get_indexer_for([target_data.index[0]])
for d in range(u, u + testing_size * (len(target_data) // testing_size), testing_size):
acc_num_train_months = []
d_counter += 1
# Dates in the batch
date_range = data_full.iloc[d:d + testing_size].index
# Loop through all sizes of training sets
for num_train_month in range(1, training_sizes + 1):
# Prepare Training/Testing Datasets
X_train = full_q_df.iloc[d - (int(21 * num_train_month)):d, :-1]
y_train = full_q_df.iloc[d - (int(21 * num_train_month)):d, -1]
X_test = full_q_df.ix[date_range, :-1]
y_test = full_q_df.ix[date_range, -1]
# Fit data and make predictions
reg = RandomForestRegressor(n_estimators=128, max_features='sqrt', oob_score=True, n_jobs=-1, random_state=random_state)
reg.fit(X_train, y_train)
y_pred = reg.predict(X_test)
y_fit = reg.predict(X_train)
pred_q = y_pred
actions = X_test.ix[:, -1]
data = {'Action': actions, 'Q': pred_q}
df_pred = pd.DataFrame(data=data, index=y_test.index)
pred_actions = []
for date in date_range:
max_q = [0, -1]
for i, r in df_pred.ix[date].iterrows():
if r['Q'] > max_q[1]:
max_q = [r['Action'], r['Q']]
pred_actions.append(max_q[0])
best_actions = []
for date in date_range:
max_q = [0, -1]
for i, r in full_q_df.ix[date].iterrows():
if r['Q'] > max_q[1]:
max_q = [r[-2], r['Q']]
best_actions.append(max_q[0])
acc_num_train_months.append(accuracy_score(best_actions, pred_actions))
accs.append(np.array(acc_num_train_months))
print("Batch {0} completed....{1:.2f}%".format(d_counter, d_counter / len(range(u, u + testing_size * (len(target_data) // testing_size), testing_size))))
geo_means = np.power(reduce(lambda x,y: x*y, accs), (1/len(accs)))
arithmetic_means = reduce(lambda x,y: x+y, accs) / len(accs)
print("Geometric Means Max: {}".format((np.argmax(geo_means) + 1, np.max(geo_means))))
print("Arithemtic Means Max: {}".format((np.argmax(arithmetic_means) + 1, np.max(arithmetic_means))))
print("Grid search best num_train_year took {} seconds:".format(time.time() - start_time))
return (geo_means, arithmetic_means)
In [1046]:
means = find_best_training_size(data_full=data_full, full_q_df=god_chimp_q_df, training_sizes=120, testing_size=7, target_data=validation_phase_data, random_state=0)
geo_means = means[0]
arithmetic_means = means[1]
Batch 1 completed....0.01%
Geometric Means Max: (64, 0.7142857142857143)
Arithemtic Means Max: (64, 0.7142857142857143)
Batch 2 completed....0.01%
Geometric Means Max: (3, 0.5714285714285714)
Arithemtic Means Max: (2, 0.5714285714285714)
Batch 3 completed....0.02%
Geometric Means Max: (96, 0.6256455914125556)
Arithemtic Means Max: (96, 0.66666666666666663)
Batch 4 completed....0.02%
Geometric Means Max: (64, 0.62865124056670951)
Arithemtic Means Max: (26, 0.6428571428571429)
Batch 5 completed....0.03%
Geometric Means Max: (64, 0.61676569768093636)
Arithemtic Means Max: (26, 0.62857142857142867)
Batch 6 completed....0.03%
Geometric Means Max: (99, 0.62103954569315234)
Arithemtic Means Max: (86, 0.6428571428571429)
Batch 7 completed....0.04%
Geometric Means Max: (75, 0.59791895257491678)
Arithemtic Means Max: (75, 0.61224489795918369)
Batch 8 completed....0.04%
Geometric Means Max: (86, 0.58377634280084301)
Arithemtic Means Max: (86, 0.6071428571428571)
Batch 9 completed....0.05%
Geometric Means Max: (86, 0.56406972935286603)
Arithemtic Means Max: (86, 0.58730158730158732)
Batch 10 completed....0.06%
Geometric Means Max: (86, 0.57754617386855167)
Arithemtic Means Max: (86, 0.59999999999999998)
Batch 11 completed....0.06%
Geometric Means Max: (86, 0.58881149457503434)
Arithemtic Means Max: (86, 0.61038961038961037)
Batch 12 completed....0.07%
Geometric Means Max: (86, 0.5734297104905578)
Arithemtic Means Max: (86, 0.59523809523809523)
Batch 13 completed....0.07%
Geometric Means Max: (19, 0.57272798013191006)
Arithemtic Means Max: (19, 0.5934065934065933)
Batch 14 completed....0.08%
Geometric Means Max: (19, 0.56098822364309964)
Arithemtic Means Max: (19, 0.58163265306122436)
Batch 15 completed....0.08%
Geometric Means Max: (19, 0.55100859829002813)
Arithemtic Means Max: (19, 0.57142857142857129)
Batch 16 completed....0.09%
Geometric Means Max: (22, 0.53490979743126044)
Arithemtic Means Max: (6, 0.5535714285714286)
Batch 17 completed....0.09%
Geometric Means Max: (22, 0.54408691643996165)
Arithemtic Means Max: (6, 0.56302521008403361)
Batch 18 completed....0.10%
Geometric Means Max: (22, 0.54557098369822032)
Arithemtic Means Max: (6, 0.56349206349206349)
Batch 19 completed....0.11%
Geometric Means Max: (22, 0.55869872780346663)
Arithemtic Means Max: (6, 0.5714285714285714)
Batch 20 completed....0.11%
Geometric Means Max: (6, 0.56378168119990191)
Arithemtic Means Max: (6, 0.58571428571428563)
Batch 21 completed....0.12%
Geometric Means Max: (22, 0.56587991561770867)
Arithemtic Means Max: (6, 0.58503401360544216)
Batch 22 completed....0.12%
Geometric Means Max: (6, 0.57497242477007127)
Arithemtic Means Max: (6, 0.59740259740259738)
Batch 23 completed....0.13%
Geometric Means Max: (6, 0.57481788816184121)
Arithemtic Means Max: (6, 0.59627329192546585)
Batch 24 completed....0.13%
Geometric Means Max: (6, 0.56782888454738434)
Arithemtic Means Max: (6, 0.5892857142857143)
Batch 25 completed....0.14%
Geometric Means Max: (22, 0.55386919150437219)
Arithemtic Means Max: (6, 0.57714285714285718)
Batch 26 completed....0.14%
Geometric Means Max: (22, 0.56325011044611106)
Arithemtic Means Max: (6, 0.58791208791208793)
Batch 27 completed....0.15%
Geometric Means Max: (22, 0.56355091864686091)
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Grid search best num_train_year took 22549.8151841 seconds:
In [1048]:
print(geo_means)
print(sorted(range(len(geo_means)), key=lambda k: geo_means[k], reverse=True))
print(arithmetic_means)
print(sorted(range(len(arithmetic_means)), key=lambda k: arithmetic_means[k], reverse=True))
validation_phase_data['Trade Price'].plot()
plt.figure()
plt.plot(geo_means)
plt.figure()
plt.plot(arithmetic_means)
[ 0.46941488 0. 0.46812252 0. 0. 0. 0.
0. 0.46291511 0.47041653 0.46304303 0. 0.45957992
0. 0.4666322 0.47626914 0. 0.48214285 0. 0.
0. 0.48211332 0. 0. 0.48167617 0. 0.
0. 0. 0.47306257 0.4742388 0. 0.46818833
0. 0.48574901 0.47116956 0.48761289 0. 0.45552042
0.47488147 0. 0. 0. 0.47865849 0.46048357
0. 0.46888289 0. 0. 0.45852544 0.
0.45188303 0.45495606 0.45458731 0. 0. 0.45398097
0. 0. 0. 0.47279696 0.44708424 0.47766806
0. 0.45651616 0. 0.47028094 0. 0. 0.
0.44763883 0. 0.47323469 0. 0. 0.45097461
0.46573407 0.44087702 0.46764007 0.4366769 0. 0. 0.
0. 0. 0.46308693 0.45887766 0. 0. 0.
0.45345877 0. 0.47053841 0.46407285 0. 0.46038203
0. 0. 0. 0. 0. 0.45663992
0.45515121 0. 0.46483863 0. 0. 0.45141788
0. 0. 0.44604973 0. 0. 0.
0.47038701 0. 0. 0.4573022 0.46905104 0.45768709]
[36, 34, 17, 21, 24, 43, 62, 15, 39, 30, 72, 29, 60, 35, 92, 9, 114, 66, 0, 118, 46, 32, 2, 78, 14, 76, 104, 93, 85, 10, 8, 44, 95, 12, 86, 49, 119, 117, 101, 64, 38, 102, 52, 53, 56, 90, 51, 107, 75, 70, 61, 110, 77, 79, 1, 3, 4, 5, 6, 7, 11, 13, 16, 18, 19, 20, 22, 23, 25, 26, 27, 28, 31, 33, 37, 40, 41, 42, 45, 47, 48, 50, 54, 55, 57, 58, 59, 63, 65, 67, 68, 69, 71, 73, 74, 80, 81, 82, 83, 84, 87, 88, 89, 91, 94, 96, 97, 98, 99, 100, 103, 105, 106, 108, 109, 111, 112, 113, 115, 116]
[ 0.50079365 0.51746032 0.50634921 0.50714286 0.48253968 0.50634921
0.50555556 0.48968254 0.4952381 0.5015873 0.50238095 0.51507937
0.49444444 0.49603175 0.50634921 0.51111111 0.51269841 0.51269841
0.51984127 0.50714286 0.50079365 0.51825397 0.51984127 0.4984127
0.51111111 0.49761905 0.49761905 0.50238095 0.51349206 0.51031746
0.51111111 0.50634921 0.50793651 0.49761905 0.52142857 0.51031746
0.51904762 0.49206349 0.49285714 0.51031746 0.5 0.49047619
0.49285714 0.51269841 0.49603175 0.49920635 0.5031746 0.50714286
0.49761905 0.49444444 0.49761905 0.48730159 0.49285714 0.49444444
0.49206349 0.4952381 0.49126984 0.48888889 0.49444444 0.50396825
0.50952381 0.48174603 0.51190476 0.49761905 0.49603175 0.51349206
0.50396825 0.48888889 0.48809524 0.48095238 0.48650794 0.5015873
0.51031746 0.47777778 0.50873016 0.48730159 0.5015873 0.48492063
0.50555556 0.47063492 0.49603175 0.49603175 0.49761905 0.47460317
0.50634921 0.49920635 0.49444444 0.51269841 0.49126984 0.49603175
0.49365079 0.49920635 0.5015873 0.4984127 0.52539683 0.49603175
0.49444444 0.45952381 0.48888889 0.47301587 0.49920635 0.49365079
0.49603175 0.5 0.50079365 0.51349206 0.48571429 0.48968254
0.47063492 0.49761905 0.48174603 0.47857143 0.46825397 0.49126984
0.50079365 0.49047619 0.46666667 0.4968254 0.50396825 0.49365079]
[94, 34, 18, 22, 36, 21, 1, 11, 105, 65, 28, 17, 43, 87, 16, 62, 24, 30, 15, 29, 72, 39, 35, 60, 74, 32, 47, 19, 3, 2, 5, 84, 31, 14, 6, 78, 118, 59, 66, 46, 27, 10, 92, 71, 76, 9, 114, 0, 104, 20, 103, 40, 85, 45, 91, 100, 93, 23, 48, 82, 63, 26, 25, 33, 109, 50, 117, 64, 80, 13, 89, 95, 44, 81, 102, 55, 8, 53, 49, 58, 86, 12, 96, 101, 90, 119, 38, 52, 42, 54, 37, 113, 88, 56, 115, 41, 7, 107, 67, 98, 57, 68, 51, 75, 70, 106, 77, 4, 110, 61, 69, 111, 73, 83, 99, 79, 108, 112, 116, 97]
Out[1048]:
[<matplotlib.lines.Line2D at 0x7fb7b4e1c790>]
We can see a trend of accuracies going up and then down again. Here we choose 35 months of data to build our model.
In [142]:
import sys
def chimp_simulate(data_full, target_data, num_iter, train_size, batch_size, random_state=0):
pv_history_list = []
action_lists = []
# Initiating data and the chimp
start_date = target_data.index[0]
end_date = target_data.index[-1]
dfFull = data_full
date_range = target_data.index[:] # Using 7 months of data to predict one month
print(date_range)
batch_count = 0
cash = 1000
share = 0
pv = 0
now_yes_share = 0
for batch in range(len(target_data) // batch_size + 1):
# for date in date_range:
batch_count += 1
print("Batch {}".format(batch_count))
try:
dfTest = dfFull.ix[target_data.index[batch * batch_size]:target_data.index[batch * batch_size + batch_size - 1]]
except IndexError:
print("Last batch size unmatched...but may be fine!")
try:
dfTest = dfFull.ix[target_data.index[batch * batch_size]:target_data.index[-1]]
except IndexError:
print("End of data")
return (pv_history_list, action_lists)
(u,) = dfFull.index.get_indexer_for([target_data.index[batch * batch_size]])
dfTrain = dfFull.iloc[u - (train_size):u]
chimp_train = ChimpBot(dfTrain, iter_random_rounds=num_iter, random_state=0)
for i in range(num_iter):
for l in range(len(chimp_train.env)):
# print("Train Round {0}-{1}".format(i + 1, l + 1))
chimp_train.update()
chimp_train.reset()
# Test the Chimp!
# q_df = deepcopy(chimp_train.q_df)
# q_dict = deepcopy(chimp_train.q_dict)
# q_reg = deepcopy(chimp_train.q_reg)
try:
_ = chimp_test
except NameError:
print("First time running...")
# now_yes_share = chimp_test.now_yes_share
chimp_test = ChimpBot(dfTest, iter_random_rounds=num_iter, random_state=0)
chimp_test.q_df = deepcopy(chimp_train.q_df)
chimp_test.q_dict = deepcopy(chimp_train.q_dict)
chimp_test.q_reg = deepcopy(chimp_train.q_reg)
chimp_test.epsilon = 0
# Pass the cheatsheet to the next chimp
try:
chimp_test.cash = cash
chimp_test.share = share
chimp_test.pv = pv
chimp_test.prev_states = prev_states
chimp_test.now_action = now_action
chimp_test.prev_action = prev_action
# chimp_test.prev_yes_share = prev_yes_share
chimp_test.reward = reward
chimp_test.prev_cash = prev_cash
chimp_test.prev_share = prev_share
chimp_test.prev_pv = prev_pv
chimp_test.prev_env_index = prev_env_index
except UnboundLocalError:
print("No cheatsheet to pass over yet...no worries!")
for l in range(len(chimp_test.env)):
# print("Train Round {0}-{1}".format(i + 1, l + 1))
chimp_test.update()
action_lists.append(chimp_test.action_list)
pv_history_list.append(chimp_test.cash + chimp_test.pv)
# Create cheatsheet for the next chimp
cash = chimp_test.cash
share = chimp_test.share
pv = chimp_test.pv
prev_states = chimp_test.prev_states
now_action = chimp_test.now_action
prev_action = chimp_test.prev_action
# prev_yes_share = chimp_test.prev_yes_share
prev_env_index = chimp_test.prev_env_index
reward = chimp_test.reward
prev_cash = chimp_test.prev_cash
prev_share = chimp_test.prev_share
prev_pv = chimp_test.prev_pv
if (batch + 1) % 3 == 0:
print(pv_history_list)
print(pv_history_list)
return (pv_history_list, action_lists)
In [143]:
validation_phase_data.head()
Out[143]:
-1d_Vol1
-2d_Vol1
-3d_Vol1
-4d_Vol1
-5d_Vol1
10d_Avg_Vol1
21d_Avg_Vol1
63d_Avg_Vol1
-1d_Vol2
-2d_Vol2
-3d_Vol2
-4d_Vol2
-5d_Vol2
-1d_Spread
-2d_Spread
-3d_Spread
-4d_Spread
-5d_Spread
10d_Spread
21d_Spread
63d_Spread
-1d_upperwick
-1d_lowerwick
-2d_upperwick
-2d_lowerwick
-3d_upperwick
-3d_lowerwick
-4d_upperwick
-4d_lowerwick
-5d_upperwick
-5d_lowerwick
10d_upperwick
10d_lowerwick
21d_upperwick
21d_lowerwick
63d_upperwick
63d_lowerwick
Trade Price
2006-09-25
2.0
2.0
3.0
2.0
3.0
3.0
3.0
3.0
1.0
2.0
2.0
2.0
2.0
1.0
-3.0
3.0
1.0
-1.0
1.0
1.0
4.0
1.0
2.0
3.0
2.0
3.0
0.0
1.0
4.0
2.0
1.0
5.0
0.0
5.0
2.0
5.0
0.0
36.610129
2006-09-26
4.0
2.0
2.0
3.0
2.0
3.0
3.0
3.0
3.0
1.0
2.0
2.0
2.0
-2.0
1.0
-3.0
3.0
1.0
1.0
1.0
4.0
2.0
2.0
1.0
2.0
3.0
2.0
3.0
0.0
1.0
4.0
5.0
0.0
5.0
2.0
5.0
0.0
36.602326
2006-09-27
4.0
4.0
2.0
2.0
3.0
3.0
3.0
3.0
2.0
3.0
1.0
2.0
2.0
-1.0
-2.0
1.0
-3.0
3.0
1.0
1.0
4.0
1.0
4.0
2.0
2.0
1.0
2.0
3.0
2.0
3.0
0.0
5.0
0.0
5.0
0.0
5.0
0.0
36.555499
2006-09-28
3.0
4.0
4.0
2.0
2.0
3.0
3.0
3.0
2.0
2.0
3.0
1.0
2.0
1.0
-1.0
-2.0
1.0
-3.0
1.0
1.0
3.0
3.0
2.0
1.0
4.0
2.0
2.0
1.0
2.0
3.0
2.0
5.0
0.0
5.0
4.0
5.0
4.0
36.797434
2006-09-29
2.0
3.0
4.0
4.0
2.0
3.0
3.0
3.0
1.0
2.0
2.0
3.0
1.0
2.0
1.0
-1.0
-2.0
1.0
1.0
1.0
3.0
2.0
1.0
3.0
2.0
1.0
4.0
2.0
2.0
1.0
2.0
3.0
1.0
3.0
4.0
3.0
5.0
36.649150
In [1051]:
start_time = time.time()
result_list = chimp_simulate(data_full=data_full, target_data=validation_phase_data, num_iter=5000, train_size=21*35, batch_size=7, random_state=0)
print("\nSimulation for Validation set took {} seconds.".format(time.time() - start_time))
DatetimeIndex(['2006-09-25', '2006-09-26', '2006-09-27', '2006-09-28',
'2006-09-29', '2006-10-02', '2006-10-03', '2006-10-04',
'2006-10-05', '2006-10-06',
...
'2011-09-14', '2011-09-15', '2011-09-16', '2011-09-19',
'2011-09-20', '2011-09-21', '2011-09-22', '2011-09-23',
'2011-09-26', '2011-09-27'],
dtype='datetime64[ns]', length=1262, freq=None)
Batch 1
Running the first time...no prevs exist.
No reward yet...0 assigned.
First time running...
No cheatsheet to pass over yet...no worries!
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 2
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 3
Running the first time...no prevs exist.
No reward yet...0 assigned.
[1000.0, 1000.0, 998.73567099999991, 1005.2679160000001, 1001.264248, 1001.264248, 1001.264248, 1002.8991539999998, 1002.8991539999998, 991.65893799999992, 991.65893799999992, 1000.242344, 1000.242344, 1000.242344, 1000.242344, 991.45452599999999, 996.76812000000007, 980.82739000000004, 980.82739000000004, 985.93659799999989, 985.93659799999989]
Batch 4
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 5
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 6
Running the first time...no prevs exist.
No reward yet...0 assigned.
[1000.0, 1000.0, 998.73567099999991, 1005.2679160000001, 1001.264248, 1001.264248, 1001.264248, 1002.8991539999998, 1002.8991539999998, 991.65893799999992, 991.65893799999992, 1000.242344, 1000.242344, 1000.242344, 1000.242344, 991.45452599999999, 996.76812000000007, 980.82739000000004, 980.82739000000004, 985.93659799999989, 985.93659799999989, 980.82741599999974, 980.82741599999974, 991.04580599999986, 981.23616199999992, 981.23616199999992, 981.03174999999999, 981.03174999999999, 980.41866999999991, 980.21425799999986, 995.7462680000001, 995.7462680000001, 998.81174600000031, 990.63708600000018, 998.19866600000023, 998.19866600000023, 998.19866600000023, 992.06763200000034, 992.06763200000034, 988.18466200000046, 988.18466200000046, 985.11910600000033]
Batch 7
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 8
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 9
Running the first time...no prevs exist.
No reward yet...0 assigned.
[1000.0, 1000.0, 998.73567099999991, 1005.2679160000001, 1001.264248, 1001.264248, 1001.264248, 1002.8991539999998, 1002.8991539999998, 991.65893799999992, 991.65893799999992, 1000.242344, 1000.242344, 1000.242344, 1000.242344, 991.45452599999999, 996.76812000000007, 980.82739000000004, 980.82739000000004, 985.93659799999989, 985.93659799999989, 980.82741599999974, 980.82741599999974, 991.04580599999986, 981.23616199999992, 981.23616199999992, 981.03174999999999, 981.03174999999999, 980.41866999999991, 980.21425799999986, 995.7462680000001, 995.7462680000001, 998.81174600000031, 990.63708600000018, 998.19866600000023, 998.19866600000023, 998.19866600000023, 992.06763200000034, 992.06763200000034, 988.18466200000046, 988.18466200000046, 985.11910600000033, 985.11910600000033, 985.11910600000033, 972.03957200000048, 972.03957200000048, 981.64480400000036, 973.6744520000002, 968.15652400000022, 985.11908000000028, 992.47635200000036, 984.91474600000038, 984.91474600000038, 984.91474600000038, 984.91474600000038, 986.5497300000003, 986.5497300000003, 993.70264200000031, 1000.8555020000003, 1000.8555020000003, 1001.6729940000004, 1001.6729940000004, 1010.4608120000003]
Batch 10
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 11
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 12
Running the first time...no prevs exist.
No reward yet...0 assigned.
[1000.0, 1000.0, 998.73567099999991, 1005.2679160000001, 1001.264248, 1001.264248, 1001.264248, 1002.8991539999998, 1002.8991539999998, 991.65893799999992, 991.65893799999992, 1000.242344, 1000.242344, 1000.242344, 1000.242344, 991.45452599999999, 996.76812000000007, 980.82739000000004, 980.82739000000004, 985.93659799999989, 985.93659799999989, 980.82741599999974, 980.82741599999974, 991.04580599999986, 981.23616199999992, 981.23616199999992, 981.03174999999999, 981.03174999999999, 980.41866999999991, 980.21425799999986, 995.7462680000001, 995.7462680000001, 998.81174600000031, 990.63708600000018, 998.19866600000023, 998.19866600000023, 998.19866600000023, 992.06763200000034, 992.06763200000034, 988.18466200000046, 988.18466200000046, 985.11910600000033, 985.11910600000033, 985.11910600000033, 972.03957200000048, 972.03957200000048, 981.64480400000036, 973.6744520000002, 968.15652400000022, 985.11908000000028, 992.47635200000036, 984.91474600000038, 984.91474600000038, 984.91474600000038, 984.91474600000038, 986.5497300000003, 986.5497300000003, 993.70264200000031, 1000.8555020000003, 1000.8555020000003, 1001.6729940000004, 1001.6729940000004, 1010.4608120000003, 1010.4608120000003, 1019.0442960000003, 1019.0442960000003, 1019.0442960000003, 1019.0442960000003, 1021.3082980000003, 1021.3082980000003, 1013.0756840000003, 1016.3687400000003, 1012.2523940000001, 1019.4559540000002, 1023.7781420000002, 1017.1920300000003, 1025.4246440000002, 1025.4246440000002, 1019.6617960000003, 1032.2165460000003, 1050.7400900000002, 1050.7400900000002, 1061.6483380000002, 1058.5610460000003]
Batch 13
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 14
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 15
Running the first time...no prevs exist.
No reward yet...0 assigned.
[1000.0, 1000.0, 998.73567099999991, 1005.2679160000001, 1001.264248, 1001.264248, 1001.264248, 1002.8991539999998, 1002.8991539999998, 991.65893799999992, 991.65893799999992, 1000.242344, 1000.242344, 1000.242344, 1000.242344, 991.45452599999999, 996.76812000000007, 980.82739000000004, 980.82739000000004, 985.93659799999989, 985.93659799999989, 980.82741599999974, 980.82741599999974, 991.04580599999986, 981.23616199999992, 981.23616199999992, 981.03174999999999, 981.03174999999999, 980.41866999999991, 980.21425799999986, 995.7462680000001, 995.7462680000001, 998.81174600000031, 990.63708600000018, 998.19866600000023, 998.19866600000023, 998.19866600000023, 992.06763200000034, 992.06763200000034, 988.18466200000046, 988.18466200000046, 985.11910600000033, 985.11910600000033, 985.11910600000033, 972.03957200000048, 972.03957200000048, 981.64480400000036, 973.6744520000002, 968.15652400000022, 985.11908000000028, 992.47635200000036, 984.91474600000038, 984.91474600000038, 984.91474600000038, 984.91474600000038, 986.5497300000003, 986.5497300000003, 993.70264200000031, 1000.8555020000003, 1000.8555020000003, 1001.6729940000004, 1001.6729940000004, 1010.4608120000003, 1010.4608120000003, 1019.0442960000003, 1019.0442960000003, 1019.0442960000003, 1019.0442960000003, 1021.3082980000003, 1021.3082980000003, 1013.0756840000003, 1016.3687400000003, 1012.2523940000001, 1019.4559540000002, 1023.7781420000002, 1017.1920300000003, 1025.4246440000002, 1025.4246440000002, 1019.6617960000003, 1032.2165460000003, 1050.7400900000002, 1050.7400900000002, 1061.6483380000002, 1058.5610460000003, 1048.0644300000004, 1043.3306620000003, 1057.9436240000002, 1073.3798760000004, 1079.1427240000003, 1073.3798760000004, 1073.9972980000002, 1074.8205880000003, 1079.1427240000003, 1073.3798760000004, 1062.8831820000003, 1063.2948400000002, 1073.7915340000004, 1083.4648600000003, 1083.4648600000003, 1083.4648600000003, 1091.2859200000003, 1091.6975520000001, 1091.6975520000001, 1079.142724, 1079.142724]
Batch 16
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 17
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 18
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 19
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 20
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 21
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 22
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 23
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 24
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 25
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 26
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 27
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 28
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 29
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 30
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 31
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 32
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 33
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 34
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 35
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 36
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 37
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 38
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 39
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 40
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 41
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 42
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 43
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 44
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 45
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 46
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 47
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 48
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 49
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 50
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 51
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 52
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 53
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 54
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 55
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 56
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 57
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 58
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 59
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 60
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 61
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 62
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 63
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 64
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 65
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 66
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 67
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 68
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 69
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 70
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 71
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 72
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 73
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 74
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 75
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 76
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 77
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 78
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 79
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 80
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 81
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 82
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 83
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 84
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 85
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 86
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 87
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 88
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 89
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 90
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 91
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 92
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 93
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 94
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 95
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 96
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 97
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 98
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 99
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 100
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 101
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 102
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 103
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 104
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 105
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 106
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 107
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 108
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 109
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 110
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 111
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 112
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 113
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 114
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 115
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 116
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 117
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 118
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 119
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 120
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 121
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 122
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 123
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 124
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 125
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 126
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 127
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 128
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 129
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 130
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 131
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 132
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 133
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 134
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 135
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 136
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 137
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 138
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 139
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 140
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 141
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 142
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No reward yet...0 assigned.
Batch 143
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 144
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 145
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No reward yet...0 assigned.
Batch 146
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 147
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 148
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 149
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 150
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 151
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 152
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 153
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 154
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No reward yet...0 assigned.
Batch 155
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 156
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 157
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No reward yet...0 assigned.
Batch 158
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 159
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 160
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 161
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 162
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 163
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Batch 164
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Batch 165
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 166
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 167
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 168
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 169
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No reward yet...0 assigned.
Batch 170
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 171
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 172
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 173
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 174
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 175
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No reward yet...0 assigned.
Batch 176
Running the first time...no prevs exist.
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Batch 177
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 178
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 179
Running the first time...no prevs exist.
No reward yet...0 assigned.
Batch 180
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 181
Last batch size unmatched...but that's fine!
Running the first time...no prevs exist.
No reward yet...0 assigned.
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4192.7708649999968]
Simulation for Validation set took 144136.679341 seconds.
In [1053]:
pv_history_list = result_list[0]
temp_pv_list = [1000]
temp_pv_list.extend(pv_history_list)
pv_history_list = temp_pv_list
plt.figure(figsize=(8,6))
validation_phase_data['Trade Price'].plot()
plt.figure(figsize=(8,6))
plt.plot(pv_history_list)
monkey_x = np.arange(len(pv_history_list))
monkey_y = ((872.08 - 1000)/ len(pv_history_list)) * monkey_x + 1000
plt.plot(monkey_x, monkey_y)
pt_x = np.arange(len(pv_history_list))
pt_y = ((751.87 - 1000)/ len(pv_history_list)) * pt_x + 1000
plt.plot(pt_x, pt_y)
Out[1053]:
[<matplotlib.lines.Line2D at 0x7fb7bc1c0310>]
The result turns out to be really good!
And if we look at the equivalent annual ROI:
$$ ROI = (1 + r)^{1262/252} = 4.1928 $$$$ \Longrightarrow r = 0.3313846 \approx 33.14\% $$The result is quite impressive compare to the Patient Trader (-5.54%) and the Monkey (-2.70%). Let's give the test set a shot!
In [144]:
test_phase_data.head()
Out[144]:
-1d_Vol1
-2d_Vol1
-3d_Vol1
-4d_Vol1
-5d_Vol1
10d_Avg_Vol1
21d_Avg_Vol1
63d_Avg_Vol1
-1d_Vol2
-2d_Vol2
-3d_Vol2
-4d_Vol2
-5d_Vol2
-1d_Spread
-2d_Spread
-3d_Spread
-4d_Spread
-5d_Spread
10d_Spread
21d_Spread
63d_Spread
-1d_upperwick
-1d_lowerwick
-2d_upperwick
-2d_lowerwick
-3d_upperwick
-3d_lowerwick
-4d_upperwick
-4d_lowerwick
-5d_upperwick
-5d_lowerwick
10d_upperwick
10d_lowerwick
21d_upperwick
21d_lowerwick
63d_upperwick
63d_lowerwick
Trade Price
2011-09-26
4.0
5.0
4.0
3.0
3.0
4.0
4.0
3.0
2.0
4.0
3.0
2.0
2.0
4.0
-1.0
-5.0
-3.0
-2.0
-1.0
-3.0
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2.0
1.0
2.0
4.0
2.0
1.0
1.0
1.0
2.0
2.0
5.0
0.0
4.0
0.0
5.0
0.0
27.491809
2011-09-27
4.0
4.0
5.0
4.0
3.0
4.0
4.0
3.0
3.0
2.0
4.0
3.0
2.0
5.0
4.0
-1.0
-5.0
-3.0
-1.0
-1.0
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27.422319
2011-09-28
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26.466837
2011-09-29
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2011-09-30
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26.162822
In [145]:
plt.figure(figsize=(8,6))
test_phase_data['Trade Price'].plot()
Out[145]:
<matplotlib.axes._subplots.AxesSubplot at 0x7fd0c05b7910>
In [146]:
start_time = time.time()
result_list = chimp_simulate(data_full=data_full, target_data=test_phase_data, num_iter=5000, train_size=21*35, batch_size=7, random_state=0)
print("\nSimulation for Test set took {} seconds.".format(time.time() - start_time))
DatetimeIndex(['2011-09-26', '2011-09-27', '2011-09-28', '2011-09-29',
'2011-09-30', '2011-10-03', '2011-10-04', '2011-10-05',
'2011-10-06', '2011-10-07',
...
'2016-09-14', '2016-09-15', '2016-09-16', '2016-09-19',
'2016-09-20', '2016-09-21', '2016-09-22', '2016-09-23',
'2016-09-26', '2016-09-27'],
dtype='datetime64[ns]', length=1260, freq=None)
Batch 1
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Batch 2
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Batch 3
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[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 970.02358199999992]
Batch 4
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Batch 5
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Batch 6
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[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 970.02358199999992, 970.02358199999992, 989.97610799999995, 989.97610799999995, 989.97610799999995, 989.97610799999995, 932.49306799999988, 958.57076400000005, 958.57076400000005, 958.57076400000005, 966.14170800000011, 966.14170800000011, 966.14170800000011, 971.92509000000018, 971.92509000000018, 971.92509000000018, 971.92509000000018, 936.35742600000015, 936.35742600000015, 936.35742600000015, 936.35742600000015, 921.02277100000015]
Batch 7
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Batch 8
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Batch 9
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[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 970.02358199999992, 970.02358199999992, 989.97610799999995, 989.97610799999995, 989.97610799999995, 989.97610799999995, 932.49306799999988, 958.57076400000005, 958.57076400000005, 958.57076400000005, 966.14170800000011, 966.14170800000011, 966.14170800000011, 971.92509000000018, 971.92509000000018, 971.92509000000018, 971.92509000000018, 936.35742600000015, 936.35742600000015, 936.35742600000015, 936.35742600000015, 921.02277100000015, 889.43334600000014, 889.43334600000014, 889.43334600000014, 871.55750600000033, 943.35874000000024, 943.35874000000024, 943.35874000000024, 943.35874000000024, 935.50744400000031, 935.50744400000031, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 890.68646600000011, 890.68646600000011, 934.3507460000003, 934.3507460000003, 934.3507460000003]
Batch 10
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Batch 12
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[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 970.02358199999992, 970.02358199999992, 989.97610799999995, 989.97610799999995, 989.97610799999995, 989.97610799999995, 932.49306799999988, 958.57076400000005, 958.57076400000005, 958.57076400000005, 966.14170800000011, 966.14170800000011, 966.14170800000011, 971.92509000000018, 971.92509000000018, 971.92509000000018, 971.92509000000018, 936.35742600000015, 936.35742600000015, 936.35742600000015, 936.35742600000015, 921.02277100000015, 889.43334600000014, 889.43334600000014, 889.43334600000014, 871.55750600000033, 943.35874000000024, 943.35874000000024, 943.35874000000024, 943.35874000000024, 935.50744400000031, 935.50744400000031, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 890.68646600000011, 890.68646600000011, 934.3507460000003, 934.3507460000003, 934.3507460000003, 934.3507460000003, 919.68204200000048, 909.35969300000033, 930.27607500000045, 925.65822200000036, 972.65233100000046, 978.67153900000039, 998.64415700000029, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 1000.2151340000004, 1011.6003440000003, 1011.6003440000003, 1011.6003440000003, 1010.0116640000003]
Batch 13
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Batch 15
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[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 970.02358199999992, 970.02358199999992, 989.97610799999995, 989.97610799999995, 989.97610799999995, 989.97610799999995, 932.49306799999988, 958.57076400000005, 958.57076400000005, 958.57076400000005, 966.14170800000011, 966.14170800000011, 966.14170800000011, 971.92509000000018, 971.92509000000018, 971.92509000000018, 971.92509000000018, 936.35742600000015, 936.35742600000015, 936.35742600000015, 936.35742600000015, 921.02277100000015, 889.43334600000014, 889.43334600000014, 889.43334600000014, 871.55750600000033, 943.35874000000024, 943.35874000000024, 943.35874000000024, 943.35874000000024, 935.50744400000031, 935.50744400000031, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 890.68646600000011, 890.68646600000011, 934.3507460000003, 934.3507460000003, 934.3507460000003, 934.3507460000003, 919.68204200000048, 909.35969300000033, 930.27607500000045, 925.65822200000036, 972.65233100000046, 978.67153900000039, 998.64415700000029, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 1000.2151340000004, 1011.6003440000003, 1011.6003440000003, 1011.6003440000003, 1010.0116640000003, 1007.0992640000003, 1007.0992640000003, 1001.8037840000003, 1009.4822240000002, 1017.4253540000003, 1017.4253540000003, 1017.4253540000003, 1013.7185540000002, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 996.84371300000043, 996.84371300000043, 996.84371300000043, 996.84371300000043, 996.58773000000053, 986.6058430000005, 986.6058430000005, 981.23089600000048]
Batch 16
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Batch 17
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Batch 18
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[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 970.02358199999992, 970.02358199999992, 989.97610799999995, 989.97610799999995, 989.97610799999995, 989.97610799999995, 932.49306799999988, 958.57076400000005, 958.57076400000005, 958.57076400000005, 966.14170800000011, 966.14170800000011, 966.14170800000011, 971.92509000000018, 971.92509000000018, 971.92509000000018, 971.92509000000018, 936.35742600000015, 936.35742600000015, 936.35742600000015, 936.35742600000015, 921.02277100000015, 889.43334600000014, 889.43334600000014, 889.43334600000014, 871.55750600000033, 943.35874000000024, 943.35874000000024, 943.35874000000024, 943.35874000000024, 935.50744400000031, 935.50744400000031, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 890.68646600000011, 890.68646600000011, 934.3507460000003, 934.3507460000003, 934.3507460000003, 934.3507460000003, 919.68204200000048, 909.35969300000033, 930.27607500000045, 925.65822200000036, 972.65233100000046, 978.67153900000039, 998.64415700000029, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 1000.2151340000004, 1011.6003440000003, 1011.6003440000003, 1011.6003440000003, 1010.0116640000003, 1007.0992640000003, 1007.0992640000003, 1001.8037840000003, 1009.4822240000002, 1017.4253540000003, 1017.4253540000003, 1017.4253540000003, 1013.7185540000002, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 996.84371300000043, 996.84371300000043, 996.84371300000043, 996.84371300000043, 996.58773000000053, 986.6058430000005, 986.6058430000005, 981.23089600000048, 1001.1947860000004, 1005.0339220000004, 1005.8018130000005, 1034.7236870000004, 1041.3783460000004, 1035.4916070000004, 1035.4916070000004, 1035.4916070000004, 1048.0329180000003, 1063.1337400000002, 1050.5924290000003, 1050.5924290000003, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004]
Batch 19
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Batch 21
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[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 970.02358199999992, 970.02358199999992, 989.97610799999995, 989.97610799999995, 989.97610799999995, 989.97610799999995, 932.49306799999988, 958.57076400000005, 958.57076400000005, 958.57076400000005, 966.14170800000011, 966.14170800000011, 966.14170800000011, 971.92509000000018, 971.92509000000018, 971.92509000000018, 971.92509000000018, 936.35742600000015, 936.35742600000015, 936.35742600000015, 936.35742600000015, 921.02277100000015, 889.43334600000014, 889.43334600000014, 889.43334600000014, 871.55750600000033, 943.35874000000024, 943.35874000000024, 943.35874000000024, 943.35874000000024, 935.50744400000031, 935.50744400000031, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 890.68646600000011, 890.68646600000011, 934.3507460000003, 934.3507460000003, 934.3507460000003, 934.3507460000003, 919.68204200000048, 909.35969300000033, 930.27607500000045, 925.65822200000036, 972.65233100000046, 978.67153900000039, 998.64415700000029, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 1000.2151340000004, 1011.6003440000003, 1011.6003440000003, 1011.6003440000003, 1010.0116640000003, 1007.0992640000003, 1007.0992640000003, 1001.8037840000003, 1009.4822240000002, 1017.4253540000003, 1017.4253540000003, 1017.4253540000003, 1013.7185540000002, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 996.84371300000043, 996.84371300000043, 996.84371300000043, 996.84371300000043, 996.58773000000053, 986.6058430000005, 986.6058430000005, 981.23089600000048, 1001.1947860000004, 1005.0339220000004, 1005.8018130000005, 1034.7236870000004, 1041.3783460000004, 1035.4916070000004, 1035.4916070000004, 1035.4916070000004, 1048.0329180000003, 1063.1337400000002, 1050.5924290000003, 1050.5924290000003, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1063.8399400000005, 1050.0717440000005, 1057.1853180000003, 1057.1853180000003, 1048.0796180000002, 1025.6487930000003, 1025.6487930000003, 1015.2550590000003, 993.77474300000017, 1018.0267110000002, 1018.0267110000002, 1018.0267110000002, 1018.0267110000002, 1018.0267110000002, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001]
Batch 22
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[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 937.77695799999992, 970.02358199999992, 970.02358199999992, 989.97610799999995, 989.97610799999995, 989.97610799999995, 989.97610799999995, 932.49306799999988, 958.57076400000005, 958.57076400000005, 958.57076400000005, 966.14170800000011, 966.14170800000011, 966.14170800000011, 971.92509000000018, 971.92509000000018, 971.92509000000018, 971.92509000000018, 936.35742600000015, 936.35742600000015, 936.35742600000015, 936.35742600000015, 921.02277100000015, 889.43334600000014, 889.43334600000014, 889.43334600000014, 871.55750600000033, 943.35874000000024, 943.35874000000024, 943.35874000000024, 943.35874000000024, 935.50744400000031, 935.50744400000031, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 887.15513200000032, 890.68646600000011, 890.68646600000011, 934.3507460000003, 934.3507460000003, 934.3507460000003, 934.3507460000003, 919.68204200000048, 909.35969300000033, 930.27607500000045, 925.65822200000036, 972.65233100000046, 978.67153900000039, 998.64415700000029, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 989.88904400000035, 1000.2151340000004, 1011.6003440000003, 1011.6003440000003, 1011.6003440000003, 1010.0116640000003, 1007.0992640000003, 1007.0992640000003, 1001.8037840000003, 1009.4822240000002, 1017.4253540000003, 1017.4253540000003, 1017.4253540000003, 1013.7185540000002, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 1006.5697040000003, 996.84371300000043, 996.84371300000043, 996.84371300000043, 996.84371300000043, 996.58773000000053, 986.6058430000005, 986.6058430000005, 981.23089600000048, 1001.1947860000004, 1005.0339220000004, 1005.8018130000005, 1034.7236870000004, 1041.3783460000004, 1035.4916070000004, 1035.4916070000004, 1035.4916070000004, 1048.0329180000003, 1063.1337400000002, 1050.5924290000003, 1050.5924290000003, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1055.1200860000004, 1063.8399400000005, 1050.0717440000005, 1057.1853180000003, 1057.1853180000003, 1048.0796180000002, 1025.6487930000003, 1025.6487930000003, 1015.2550590000003, 993.77474300000017, 1018.0267110000002, 1018.0267110000002, 1018.0267110000002, 1018.0267110000002, 1018.0267110000002, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001, 1003.9374410000001, 993.72141599999998, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 985.72624099999996, 964.93876099999977, 924.16348099999971, 924.16348099999971, 924.16348099999971, 965.47178699999972, 972.35648399999968, 964.3702949999996]
Batch 25
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 26
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 27
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 28
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 29
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 30
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 31
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 32
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 33
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 34
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 35
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 36
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 37
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 38
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 39
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 40
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 41
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 42
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 43
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 44
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 45
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 46
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 47
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 48
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 49
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 50
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 51
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 52
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 53
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 54
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 55
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 56
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 57
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 58
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 59
Running the first time...no prevs exist.
No reward yet...0 assigned.
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Batch 60
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 61
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 62
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 63
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 64
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 65
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 66
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 67
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 68
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 69
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 70
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 71
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 72
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 73
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 74
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 75
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 76
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 77
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 78
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 79
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 80
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 81
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 82
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 83
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 84
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 85
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 86
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 87
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 88
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 89
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 90
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 91
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 92
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 93
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 94
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 95
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 96
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 97
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 98
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 99
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 100
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 101
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 102
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 103
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 104
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 105
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 106
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 107
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 108
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 109
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 110
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 111
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 112
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 113
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 114
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 115
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 116
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 117
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 118
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 119
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 120
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 121
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 122
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 123
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 124
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 125
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 126
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 127
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 128
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 129
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 130
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No reward yet...0 assigned.
Updating Q model...
Batch 131
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 132
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 133
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 134
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 135
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 136
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 137
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 138
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 139
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 140
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 141
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 142
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No reward yet...0 assigned.
Updating Q model...
Batch 143
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 144
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 145
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 146
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 147
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 148
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 149
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 150
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 151
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 152
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 153
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 154
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Updating Q model...
Batch 155
Running the first time...no prevs exist.
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Updating Q model...
Batch 156
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 157
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Updating Q model...
Batch 158
Running the first time...no prevs exist.
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Updating Q model...
Batch 159
Running the first time...no prevs exist.
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Updating Q model...
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Batch 160
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 161
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 162
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 163
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Batch 164
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Batch 165
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Batch 166
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No reward yet...0 assigned.
Updating Q model...
Batch 167
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 168
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 169
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Updating Q model...
Batch 170
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Batch 171
Running the first time...no prevs exist.
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Updating Q model...
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Batch 172
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 173
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 174
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 175
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Updating Q model...
Batch 176
Running the first time...no prevs exist.
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Updating Q model...
Batch 177
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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Batch 178
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 179
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
Batch 180
Running the first time...no prevs exist.
No reward yet...0 assigned.
Updating Q model...
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1817.8574740000004, 1817.8574740000004, 1817.8574740000004, 1835.639042, 1835.639042, 1840.9180220000003, 1827.0261580000004, 1827.0261580000004, 1827.0261580000004, 1827.0261580000004, 1823.8607790000003, 1823.8607790000003, 1825.5872650000003, 1828.1771100000003, 1844.8672480000002, 1844.8672480000002, 1844.8672480000002, 1844.8672480000002, 1844.8672480000002, 1905.5151200000005, 1958.8598880000004, 1958.8598880000004, 1958.8598880000004, 1958.8598880000004, 1979.3398880000004, 1979.3398880000004, 1979.3398880000004, 1979.3398880000004, 2008.1699190000004, 2006.9298880000001, 2006.9298880000001, 2006.9298880000001, 2006.9298880000001, 2006.9298880000001, 2006.9298880000001, 1999.4898570000003, 2010.3399190000002, 2005.0698570000002, 2013.1297950000003, 2019.3299500000005, 2012.1998260000003, 2008.1699190000004, 2008.1699190000004, 2008.1699190000004, 2008.1699190000004, 2008.1699190000004, 2008.1699190000004, 2002.1697690000003, 2002.1697690000003, 2002.1697690000003, 2007.569769, 2007.569769, 2019.5697989999999, 2019.2697389999998, 2024.6697390000002, 2026.469679, 2026.469679, 2024.6697390000002, 2024.6697390000002, 2024.6697390000002, 2028.2698290000001, 2028.2698290000001, 2050.1697090000002, 2050.1697090000002, 2050.1697090000002, 2041.469679, 2041.469679, 2039.9697990000002, 2039.9697990000002, 2042.6696790000001, 2042.6696790000001, 2042.6696790000001, 2042.6696790000001, 2038.769769, 2038.769769, 2014.1697989999998, 2025.269859, 2033.3697689999997, 2033.3697689999997, 2033.3697689999997, 2029.1697989999996, 1985.0697689999997, 2002.4698289999994]
Batch 181
Last batch size unmatched...but may be fine!
End of data
Simulation for Test set took 130600.590862 seconds.
In [154]:
pv_history_list = result_list[0]
temp_pv_list = [1000]
temp_pv_list.extend(pv_history_list)
pv_history_list = temp_pv_list
plt.figure(figsize=(6,4))
test_phase_data['Trade Price'].plot()
plt.figure(figsize=(6,4))
plt.plot(pv_history_list, label='Chimp')
monkey_x = np.arange(len(pv_history_list))
monkey_y = ((1542.635 - 1000)/ len(pv_history_list)) * monkey_x + 1000
plt.plot(monkey_x, monkey_y, label='Monkey')
pt_x = np.arange(len(pv_history_list))
pt_y = ((2399.255 - 1000)/ len(pv_history_list)) * monkey_x + 1000
plt.plot(pt_x, pt_y, label='Patient Trader')
plt.legend()
Out[154]:
<matplotlib.legend.Legend at 0x7fd0995cac90>
In [1058]:
def inverse_percentile(arr, num):
arr = sorted(arr)
i_arr = [i for i, x in enumerate(arr) if x > num]
return i_arr[0] / len(arr) if len(i_arr) > 0 else 1
print(inverse_percentile(monkey_test.pv_history_list, 2002.4698289999994))
0.81995
The result turns out to be above the median by quite a lot (above 82% of the Monkeys).
And when we look at the equivalent annual ROI:
$$ ROI = (1 + r)^{1260/252} = 2.0025 $$$$ \Longrightarrow r = 0.1489854 \approx 14.90\% $$It is certainly not as impressive as what she did on the cross-validation dataset which means we have probably overfitted the cv dataset with the grid search. Although it is above about 82% of the Monkeys (with median equal to 9.06%), it can still be pure chance and plus, with all the effort, it still can't beat the PT (19.13%). Let's try to refine it a bit.
Surely we wouldn't expect the Chimp to give us a 33% of ROI on the test dataset when there is 2008 financial crisis, which though not impossible, is quite unlikely. However there surely is room for improvement. One way to refine it is to do it on the reinforcement learning part. It could be that the God Chimp is doing her job way too well. We can think of the God Chimp as someone who can see the future. And if you think about it: 1. we have someone who can see the future, 2. there's no trading cost. This means this "someone" will make use of every possible ups and downs to make all the money he or she wishes to. And this is bad, because he or she can make money out of the noise too, and we can't model the noise. If most of the time our model is trying to fit the noise, then it's not very good.
So to fix this, we can introduce trading cost on the training stage so if it were just small ups and downs, the Chimp would refrain herself from being too greedy or she would be penalized by the trading cost.
In [157]:
class MonkeyBot(object):
def __init__(self, dfEnv, cash=1000, share=0, pv=0, random_state=0):
random.seed(random_state)
np.random.seed(random_state)
self.cash = cash
self.share = share
self.pv = pv
self.asset_history_list = []
self.action_list = []
self.env = deepcopy(dfEnv)
def buy(self, stock_price, cost, fold=1):
if self.cash < stock_price:
self.hold(stock_price)
else:
num_affordable = int(self.cash // stock_price)
buy_amount = int(num_affordable // fold)
self.cash = self.cash - stock_price * buy_amount
self.share = self.share + buy_amount
self.pv = stock_price * self.share
# Adding transaction cost
self.trading_cost(buy_amount, cost)
# Append action to action list
self.action_list.append('Buy')
def sell(self, stock_price, cost, fold=1):
if self.share == 0:
self.hold(stock_price)
else:
sell_amount = int(self.share // fold)
self.cash = self.cash + stock_price * sell_amount
self.pv = 0
self.share = 0
# Adding transaction cost
self.trading_cost(sell_amount, cost)
self.action_list.append('Sell')
def hold(self, stock_price):
self.pv = stock_price * self.share
def trading_cost(self, trading_amount, cost):
if cost is None:
pass
elif cost == 'low':
if trading_amount * 0.01 < 1.99:
self.cash = self.cash - 1.99
else:
self.cash = self.cash - trading_amount * 0.01
elif cost == 'medium':
if trading_amount * 0.01 < 5:
self.cash = self.cash - 5
else:
self.cash = self.cash - trading_amount * 0.01
elif cost == 'high':
if trading_amount * 0.01 < 7:
self.cash = self.cash - 7
else:
self.cash = self.cash - trading_amount * 0.01
else:
raise ValueError("Invalid cost parameter!")
def reset(self):
self.cash = 1000
self.share = 0
self.pv = 0
def make_decision(self, x, cost):
random_choice = random.choice([1, 2])
if random_choice == 0:
self.hold(x)
elif random_choice == 1:
self.buy(x, cost)
elif random_choice == 2:
self.sell(x, cost)
else:
raise ValueError("Invalid choice!")
return self.pv # for frame-wise operation
def simulate(self, iters, cost=None):
start_time = time.time()
for i in range(iters):
for index, row in self.env.iterrows():
self.make_decision(row['Trade Price'], cost)
self.asset_history_list.append(self.pv + self.cash)
self.reset()
print("{0} iterations took {1} seconds".format(iters, time.time() - start_time))
return self.asset_history_list, self.action_list
In [173]:
import sys
class ChimpBot(MonkeyBot):
"""An agent that learns to drive in the smartcab world."""
def __init__(self, dfEnv, iter_random_rounds, gamma, random_state=0, test_mode=False, cash=1000, share=0, pv=0):
super(ChimpBot, self).__init__(dfEnv, iter_random_rounds, cash, share, pv)
# From MonkeyBot:
# sets self.cash = 1000
# sets self.share = 0
# sets self.pv = 0
# sets self.pv_history_list = []
# sets self.env = dfEnv
# implements buy(self, stock_price)
# implements sell(self, stock_price)
# implements hold(self)
# Set random state
self.random_state = random_state
random.seed(self.random_state)
np.random.seed(self.random_state)
# Chimp parameters
self.valid_actions = ['Buy', 'Sell']
self.gamma = gamma # Discount factor
self.epsilon = 1 # Exploration-exploitation
self.test_mode = test_mode
self.random_rounds = iter_random_rounds # Number of rounds where the bot chooses to go monkey
self.num_features = len(dfEnv.columns) # Use every columns from the input data
# Turn input data into index, row
self.iter_env = self.env.iterrows()
self.now_env_index, self.now_row = self.iter_env.next()
# Numpy alternative
# self.env_arr = self.env.values
# self.now_row = 0
# May need to put back later
# self.prev_cash = self.cash
# self.prev_share = self.share
# self.prev_pv = self.pv
# Q-table and q_df
self.q_df_columns = list(self.env.columns)
self.q_df_columns.extend(['Action', 'Q Value'])
self.q_df = pd.DataFrame(columns=self.q_df_columns)
self.q_dict = defaultdict(lambda: (0, 0)) # element of q_dict is (state, act): (q_value, t)
self.q_dict_analysis = defaultdict(lambda: (0, 0))
# Misc
self.reset_counter = 0
def make_q_df(self):
"""Make a q_df out of the q_dict."""
# print("Making q_df...")
result_dict = defaultdict(list)
for index, row in self.q_dict.iteritems():
for i in range(len(self.q_dict.keys()[0])):
column_name = 'col' + str(i + 1)
result_dict[column_name].append(index[i])
result_dict['Q'].append(self.q_dict[index][0])
self.q_df = pd.DataFrame(result_dict)
q_df_column_list = ['col' + str(x) for x in range(1, self.num_features - 1 + 1 + 1)] # features + action
q_df_column_list.append('Q')
self.q_df = self.q_df[q_df_column_list]
def transfer_action(x):
if x == 'Buy':
return 1
elif x == 'Sell':
return 2
elif x == 'Hold':
return 0
else:
raise ValueError("Wrong action!")
def str_float_int(x):
return int(float(x))
arr_int = np.vectorize(str_float_int)
# print(self.q_df.head())
self.q_df.ix[:, -2] = self.q_df.ix[:, -2].apply(transfer_action)
self.q_df.ix[:, :-1] = self.q_df.ix[:, :-1].apply(arr_int) # Maybe useless
def split_q_df(self):
"""Splitting q_df into features and labels."""
self.q_df_X = self.q_df.ix[:, :-1]
self.q_df_y = self.q_df.ix[:, -1]
def train_on_q_df(self):
"""Model the q_df."""
# print("Training on q_df...")
self.q_reg = RandomForestRegressor(n_estimators=2000, max_features='sqrt', n_jobs=-1, random_state=self.random_state)
self.q_reg = self.q_reg.fit(self.q_df_X, self.q_df_y)
def update_q_model(self):
"""1. Make q_df
2. Split q_df
3. Train on q_df
"""
# print("Updating Q model...")
# start_time = time.time()
self.make_q_df()
self.split_q_df()
self.train_on_q_df()
# print("Update took {} seconds".format(time.time() - start_time))
def from_state_action_predict_q(self, state_action):
"""Make prediction using self.reg"""
state_action = [state_action]
pred_q = self.q_reg.predict(state_action)
return pred_q
def max_q(self):
# print("Calculating Max Q")
def transfer_action(x):
if x == 'Buy':
return 1
elif x == 'Sell':
return 2
elif x == 'Hold':
return 0
else:
raise ValueError("Invalid action!")
# def str_float_int(x):
# return int(float(x))
max_q = None
q_compare_dict = {}
if len(self.now_states) != self.num_features - 1:
raise ValueError("Got ya bastard! @ MaxQ")
# Populate the q_dict
for act in set(self.valid_actions):
# added 1 more additional features to the feature set
self.now_states.append(act)
now_row_key = tuple(self.now_states)
_ = self.q_dict[now_row_key]
try:
self.q_reg
except AttributeError:
pass
# print('No q_reg yet...going with default.')
else:
if _[1] == 0:
# print("Dreaming mode...")
single_X = np.array(now_row_key)
# print(single_X)
# arr_int = np.vectorize(str_float_int)
single_X[-1] = transfer_action(single_X[-1])
# single_X = arr_int(single_X)
single_X = single_X.reshape(1, -1)
pred_q = self.q_reg.predict(single_X)
dreamed_q = (1 - (1 / (self.q_dict[now_row_key][1] + 1))) * self.q_dict[now_row_key][0] + (1 / (self.q_dict[now_row_key][1] + 1)) * pred_q[0]
self.q_dict[now_row_key] = (dreamed_q, self.q_dict[now_row_key][1] + 1)
q_compare_dict[now_row_key] = self.q_dict[now_row_key]
self.now_states.pop()
try:
key, qAndT = max(q_compare_dict.iteritems(), key=lambda x:x[1])
except ValueError:
print("Wrong Q Value in Q Compare Dict!")
sys.exit(1)
else:
return key[-1], qAndT[0], qAndT[1]
def q_update(self):
# print("Updating Q table...")
# prev_states.append(self.prev_yes_share)
self.prev_states.append(self.prev_action)
prev_states_key = tuple(self.prev_states)
if len(prev_states_key) != self.num_features - 1 + 1:
raise ValueError("Got ya bastard! @ Q_Update")
q_temp = self.q_dict[prev_states_key]
q_temp0 = (1 - (1 / (q_temp[1] + 1))) * q_temp[0] + (1 / (q_temp[1] + 1)) * (self.reward + self.gamma * self.max_q()[1])
self.q_dict[prev_states_key] = (q_temp0, q_temp[1] + 1)
# For analysis purpose
self.q_dict_analysis[prev_states_key] = (q_temp0, self.prev_env_index)
def reset(self):
# print("Resetting...")
# Portfolio change over iterations
self.asset_history_list.append(self.pv + self.cash)
self.iter_env = self.env.iterrows()
self.now_env_index, self.now_row = self.iter_env.next()
# self.now_row = 0 # Numpy option
self.cash = 1000
self.share = 0
self.pv = 0
# Delete all prevs
del self.prev_states
del self.prev_env_index
del self.prev_cash
del self.prev_share
del self.prev_pv
del self.prev_action
if self.test_mode is True:
self.epsilon = 0
else:
if self.epsilon - 1/self.random_rounds > 0.00001: # Epislon threshold: 0.01
self.epsilon = self.epsilon - 1/self.random_rounds
else:
self.epsilon = 0.00001 # Epislon threshold: 0.1
self.reset_counter += 1
if self.reset_counter % self.random_rounds == 0:
self.update_q_model()
if np.abs(self.epsilon - 0.00001) > 0.000001:
self.action_list = []
def make_decision(self):
return self.max_q()[0]
def update(self, cost):
# Update state
self.now_states = list(self.now_row)
self.now_states.pop() # Remove Trade Price
### Numpy option
# try:
# self.now_states = list(self.env_arr[self.now_row])
# except IndexError:
# print("End of data.")
# sys.exit(1)
# self.now_states.pop() # Remove Trade Price
if len(self.now_states) != self.num_features - 1:
raise ValueError("Got ya bastard! @ Q_Update...something wrong with the self.now_row!!!")
# Update Q-table using prevs
try:
self.prev_states
except AttributeError:
pass
# print("Running the first time...no prevs exist.")
else:
self.hold(self.now_row[-1])
self.reward = ((self.cash - self.prev_cash) + (self.pv - self.prev_pv)) / (self.prev_cash + self.prev_pv)
self.q_update()
# All the prev stuff!
self.prev_states = copy(self.now_states)
self.prev_env_index = deepcopy(self.now_env_index)
# self.prev_env_index = self.env.index[self.now_row] # Numpy option
self.prev_cash = self.cash
self.prev_share = self.share
self.prev_pv = self.pv
# Exploitation-exploration decisioning
self.decision = np.random.choice(2, p = [self.epsilon, 1 - self.epsilon]) # decide to go random or with the policy
# self.decision = 0 # Force random mode
# print("Random decision: {0}, Epislon: {1}".format(self.decision, self.epsilon))
if self.decision == 0: # if zero, go random
action = random.choice(self.valid_actions)
else: # else go with the policy
action = self.make_decision()
# Execute action and get reward
if action == 'Buy':
# print(self.now_row)
self.buy(self.now_row[-1], cost)
# self.buy(self.env_arr[self.now_row][-1], cost) # Numpy option
elif action == 'Sell':
# print(self.now_row)
self.sell(self.now_row[-1], cost)
# self.sell(self.env_arr[self.now_row][-1], cost) # Numpy option
elif action == 'Hold':
# print(self.now_row)
self.hold(self.now_row[-1])
# self.hold(self.env_arr[self.now_row][-1]) # Numpy option
else:
raise ValueError("Invalid action man!")
self.prev_action = action
# self.now_row += 1 # Numpy option
try:
self.now_env_index, self.now_row = self.iter_env.next()
except StopIteration:
pass
def simulate(self, cost=None):
start_time = time.time()
for i in range(self.random_rounds):
for l in range(len(self.env)):
# for l in range(len(self.env_arr)): # Numpy option
self.update(cost)
self.reset()
if (i + 1) % 500 == 0:
print(self.asset_history_list[-1])
print("Round {} finished".format(i + 1))
# print(self.asset_history_list[-1])
# print("Round {} finished".format(i + 1))
print("{0} rounds of simulation with cost = {1}, took {2} seconds".format(self.random_rounds, cost, time.time() - start_time))
return self.asset_history_list, self.action_list
In [174]:
def chimp_simulate(data_full, target_data, num_iter, gamma, train_size, batch_size, random_state=0):
pv_history_list = []
action_lists = []
# Initiating data and the chimp
start_date = target_data.index[0]
end_date = target_data.index[-1]
dfFull = data_full
date_range = target_data.index[:] # Using 7 months of data to predict one month
print(date_range)
batch_count = 0
cash = 1000
share = 0
pv = 0
now_yes_share = 0
for batch in range(len(target_data) // batch_size + 1):
# for date in date_range:
batch_count += 1
print("Batch {}".format(batch_count))
try:
dfTest = dfFull.ix[target_data.index[batch * batch_size]:target_data.index[batch * batch_size + batch_size - 1]]
except IndexError:
print("Last batch size unmatched...but may be fine!")
try:
dfTest = dfFull.ix[target_data.index[batch * batch_size]:target_data.index[-1]]
except IndexError:
print("End of data")
return (pv_history_list, action_lists)
(u,) = dfFull.index.get_indexer_for([target_data.index[batch * batch_size]])
dfTrain = dfFull.iloc[u - (train_size):u]
chimp_train = ChimpBot(dfTrain, iter_random_rounds=num_iter, gamma=gamma, random_state=0)
for i in range(num_iter):
for l in range(len(chimp_train.env)):
# print("Train Round {0}-{1}".format(i + 1, l + 1))
chimp_train.update('high')
chimp_train.reset()
# Test the Chimp!
# q_df = deepcopy(chimp_train.q_df)
# q_dict = deepcopy(chimp_train.q_dict)
# q_reg = deepcopy(chimp_train.q_reg)
try:
_ = chimp_test
except NameError:
print("First time running...")
# now_yes_share = chimp_test.now_yes_share
chimp_test = ChimpBot(dfTest, iter_random_rounds=num_iter, gamma=gamma, random_state=0)
chimp_test.q_df = deepcopy(chimp_train.q_df)
chimp_test.q_dict = deepcopy(chimp_train.q_dict)
chimp_test.q_reg = deepcopy(chimp_train.q_reg)
chimp_test.epsilon = 0
# Pass the cheatsheet to the next chimp
try:
chimp_test.cash = cash
chimp_test.share = share
chimp_test.pv = pv
chimp_test.prev_states = prev_states
# chimp_test.now_action = now_action
chimp_test.prev_action = prev_action
# chimp_test.prev_yes_share = prev_yes_share
chimp_test.reward = reward
chimp_test.prev_cash = prev_cash
chimp_test.prev_share = prev_share
chimp_test.prev_pv = prev_pv
chimp_test.prev_env_index = prev_env_index
except UnboundLocalError:
print("No cheatsheet to pass over yet...no worries!")
for l in range(len(chimp_test.env)):
# print("Train Round {0}-{1}".format(i + 1, l + 1))
chimp_test.update(None)
action_lists.append(chimp_test.action_list)
pv_history_list.append(chimp_test.cash + chimp_test.pv)
# Create cheatsheet for the next chimp
cash = chimp_test.cash
share = chimp_test.share
pv = chimp_test.pv
prev_states = chimp_test.prev_states
# now_action = chimp_test.now_action
prev_action = chimp_test.prev_action
# prev_yes_share = chimp_test.prev_yes_share
prev_env_index = chimp_test.prev_env_index
reward = chimp_test.reward
prev_cash = chimp_test.prev_cash
prev_share = chimp_test.prev_share
prev_pv = chimp_test.prev_pv
if (batch + 1) % 3 == 0:
print(pv_history_list)
print(pv_history_list)
# return (pv_history_list, action_lists)
return pv_history_list
In [176]:
# start_time = time.time()
result_list = chimp_simulate(data_full=data_full, target_data=test_phase_data, num_iter=5000, gamma=0.75, train_size=21*35, batch_size=7, random_state=0)
print("\nSimulation for Test set took {} seconds.".format(time.time() - start_time))
DatetimeIndex(['2011-09-26', '2011-09-27', '2011-09-28', '2011-09-29',
'2011-09-30', '2011-10-03', '2011-10-04', '2011-10-05',
'2011-10-06', '2011-10-07',
...
'2016-09-14', '2016-09-15', '2016-09-16', '2016-09-19',
'2016-09-20', '2016-09-21', '2016-09-22', '2016-09-23',
'2016-09-26', '2016-09-27'],
dtype='datetime64[ns]', length=1260, freq=None)
Batch 1
First time running...
No cheatsheet to pass over yet...no worries!
Batch 2
Batch 3
[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 1025.0354599999998, 1044.348352, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1066.5792769999998, 1066.5792769999998, 1066.5792769999998, 1095.1105319999999, 1104.5127500000001, 1104.5127500000001]
Batch 4
Batch 5
Batch 6
[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 1025.0354599999998, 1044.348352, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1066.5792769999998, 1066.5792769999998, 1066.5792769999998, 1095.1105319999999, 1104.5127500000001, 1104.5127500000001, 1104.5127500000001, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1062.215344, 1092.3676800000003, 1116.3598860000002, 1116.3598860000002, 1125.1137900000001, 1125.1137900000001, 1125.1137900000001, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1113.1089770000001]
Batch 7
Batch 8
Batch 9
[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 1025.0354599999998, 1044.348352, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1066.5792769999998, 1066.5792769999998, 1066.5792769999998, 1095.1105319999999, 1104.5127500000001, 1104.5127500000001, 1104.5127500000001, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1062.215344, 1092.3676800000003, 1116.3598860000002, 1116.3598860000002, 1125.1137900000001, 1125.1137900000001, 1125.1137900000001, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1113.1089770000001, 1113.1089770000001, 1116.964565, 1116.964565, 1094.3568850000001, 1185.1643280000003, 1165.9478000000001, 1165.9478000000001, 1165.9478000000001, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1129.4338330000005, 1129.4338330000005, 1129.4338330000005, 1133.9903930000003, 1133.9903930000003, 1189.5631130000004, 1193.6114930000001, 1193.6114930000001]
Batch 10
Batch 11
Batch 12
[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 1025.0354599999998, 1044.348352, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1066.5792769999998, 1066.5792769999998, 1066.5792769999998, 1095.1105319999999, 1104.5127500000001, 1104.5127500000001, 1104.5127500000001, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1062.215344, 1092.3676800000003, 1116.3598860000002, 1116.3598860000002, 1125.1137900000001, 1125.1137900000001, 1125.1137900000001, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1113.1089770000001, 1113.1089770000001, 1116.964565, 1116.964565, 1094.3568850000001, 1185.1643280000003, 1165.9478000000001, 1165.9478000000001, 1165.9478000000001, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1129.4338330000005, 1129.4338330000005, 1129.4338330000005, 1133.9903930000003, 1133.9903930000003, 1189.5631130000004, 1193.6114930000001, 1193.6114930000001, 1193.6114930000001, 1174.6841330000002, 1161.3649730000002, 1188.3538530000003, 1182.3953330000002, 1243.0328930000003, 1250.7996130000004, 1276.5707330000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1279.6950790000003, 1279.6950790000003, 1279.6950790000003, 1277.6827510000003]
Batch 13
Batch 14
Batch 15
[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 1025.0354599999998, 1044.348352, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1066.5792769999998, 1066.5792769999998, 1066.5792769999998, 1095.1105319999999, 1104.5127500000001, 1104.5127500000001, 1104.5127500000001, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1062.215344, 1092.3676800000003, 1116.3598860000002, 1116.3598860000002, 1125.1137900000001, 1125.1137900000001, 1125.1137900000001, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1113.1089770000001, 1113.1089770000001, 1116.964565, 1116.964565, 1094.3568850000001, 1185.1643280000003, 1165.9478000000001, 1165.9478000000001, 1165.9478000000001, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1129.4338330000005, 1129.4338330000005, 1129.4338330000005, 1133.9903930000003, 1133.9903930000003, 1189.5631130000004, 1193.6114930000001, 1193.6114930000001, 1193.6114930000001, 1174.6841330000002, 1161.3649730000002, 1188.3538530000003, 1182.3953330000002, 1243.0328930000003, 1250.7996130000004, 1276.5707330000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1279.6950790000003, 1279.6950790000003, 1279.6950790000003, 1277.6827510000003, 1273.9937110000003, 1273.9937110000003, 1267.2861030000001, 1277.0121270000002, 1277.0121270000002, 1277.0121270000002, 1277.0121270000002, 1272.4404070000001, 1263.6234920000004, 1263.6234920000004, 1249.2552450000005, 1241.0914540000003, 1263.6234920000004, 1263.6234920000004, 1263.6234920000004, 1283.7461260000005, 1299.5089060000003, 1299.1734800000004, 1286.0937660000004, 1300.1796820000006, 1293.1366480000004]
Batch 16
Batch 17
Batch 18
[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 1025.0354599999998, 1044.348352, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1066.5792769999998, 1066.5792769999998, 1066.5792769999998, 1095.1105319999999, 1104.5127500000001, 1104.5127500000001, 1104.5127500000001, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1062.215344, 1092.3676800000003, 1116.3598860000002, 1116.3598860000002, 1125.1137900000001, 1125.1137900000001, 1125.1137900000001, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1113.1089770000001, 1113.1089770000001, 1116.964565, 1116.964565, 1094.3568850000001, 1185.1643280000003, 1165.9478000000001, 1165.9478000000001, 1165.9478000000001, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1129.4338330000005, 1129.4338330000005, 1129.4338330000005, 1133.9903930000003, 1133.9903930000003, 1189.5631130000004, 1193.6114930000001, 1193.6114930000001, 1193.6114930000001, 1174.6841330000002, 1161.3649730000002, 1188.3538530000003, 1182.3953330000002, 1243.0328930000003, 1250.7996130000004, 1276.5707330000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1279.6950790000003, 1279.6950790000003, 1279.6950790000003, 1277.6827510000003, 1273.9937110000003, 1273.9937110000003, 1267.2861030000001, 1277.0121270000002, 1277.0121270000002, 1277.0121270000002, 1277.0121270000002, 1272.4404070000001, 1263.6234920000004, 1263.6234920000004, 1249.2552450000005, 1241.0914540000003, 1263.6234920000004, 1263.6234920000004, 1263.6234920000004, 1283.7461260000005, 1299.5089060000003, 1299.1734800000004, 1286.0937660000004, 1300.1796820000006, 1293.1366480000004, 1319.2962280000004, 1319.2962280000004, 1319.2962280000004, 1357.1938560000001, 1365.9137540000004, 1358.200096, 1321.9792180000002, 1343.1080540000003, 1359.5414960000001, 1359.5414960000001, 1343.5405130000004, 1436.6078710000002, 1442.8124380000004, 1442.8124380000004, 1442.8124380000004, 1456.4746900000002, 1456.4746900000002, 1456.4746900000002, 1456.4746900000002, 1456.4746900000002, 1488.565018]
Batch 19
Batch 20
Batch 21
[1000.0, 997.49836000000005, 963.10100799999987, 963.10100799999987, 963.10100799999987, 963.10100799999987, 1025.0354599999998, 1044.348352, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1095.6274519999997, 1066.5792769999998, 1066.5792769999998, 1066.5792769999998, 1095.1105319999999, 1104.5127500000001, 1104.5127500000001, 1104.5127500000001, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1126.8837640000002, 1062.215344, 1092.3676800000003, 1116.3598860000002, 1116.3598860000002, 1125.1137900000001, 1125.1137900000001, 1125.1137900000001, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1131.9486960000002, 1113.1089770000001, 1113.1089770000001, 1116.964565, 1116.964565, 1094.3568850000001, 1185.1643280000003, 1165.9478000000001, 1165.9478000000001, 1165.9478000000001, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1156.3790330000004, 1129.4338330000005, 1129.4338330000005, 1129.4338330000005, 1133.9903930000003, 1133.9903930000003, 1189.5631130000004, 1193.6114930000001, 1193.6114930000001, 1193.6114930000001, 1174.6841330000002, 1161.3649730000002, 1188.3538530000003, 1182.3953330000002, 1243.0328930000003, 1250.7996130000004, 1276.5707330000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1265.2738130000002, 1279.6950790000003, 1279.6950790000003, 1279.6950790000003, 1277.6827510000003, 1273.9937110000003, 1273.9937110000003, 1267.2861030000001, 1277.0121270000002, 1277.0121270000002, 1277.0121270000002, 1277.0121270000002, 1272.4404070000001, 1263.6234920000004, 1263.6234920000004, 1249.2552450000005, 1241.0914540000003, 1263.6234920000004, 1263.6234920000004, 1263.6234920000004, 1283.7461260000005, 1299.5089060000003, 1299.1734800000004, 1286.0937660000004, 1300.1796820000006, 1293.1366480000004, 1319.2962280000004, 1319.2962280000004, 1319.2962280000004, 1357.1938560000001, 1365.9137540000004, 1358.200096, 1321.9792180000002, 1343.1080540000003, 1359.5414960000001, 1359.5414960000001, 1343.5405130000004, 1436.6078710000002, 1442.8124380000004, 1442.8124380000004, 1442.8124380000004, 1456.4746900000002, 1456.4746900000002, 1456.4746900000002, 1456.4746900000002, 1456.4746900000002, 1488.565018, 1479.6686979999999, 1491.7423420000002, 1472.6786860000002, 1482.5282500000001, 1487.294218, 1474.1820099999998, 1441.8816220000001, 1439.642998, 1425.2516740000001, 1395.5096979999998, 1429.089346, 1429.089346, 1378.4089260000001, 1382.1400659999999, 1382.1400659999999, 1363.1737409999998, 1360.9973009999997, 1345.4511759999998, 1345.4511759999998, 1358.8208609999999, 1355.0898259999999]
Batch 22
Batch 23
Batch 24
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Batch 25
Batch 26
Batch 27
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Batch 28
Batch 29
Batch 30
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Batch 31
Batch 32
Batch 33
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Batch 34
Batch 35
Batch 36
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Batch 37
Batch 38
Batch 39
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Batch 40
Batch 41
Batch 42
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Batch 43
Batch 44
Batch 45
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Batch 46
Batch 47
Batch 48
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Batch 49
Batch 50
Batch 51
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Batch 52
Batch 53
Batch 54
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Batch 55
Batch 56
Batch 57
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Batch 58
Batch 59
Batch 60
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Batch 61
Batch 62
Batch 63
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Batch 64
Batch 65
Batch 66
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Batch 67
Batch 68
Batch 69
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Batch 70
Batch 71
Batch 72
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Batch 73
Batch 74
Batch 75
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Batch 76
Batch 77
Batch 78
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Batch 79
Batch 80
Batch 81
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1963.0195559999995, 1961.3497319999997]
Batch 82
Batch 83
Batch 84
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Batch 85
Batch 86
Batch 87
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Batch 88
Batch 89
Batch 90
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Batch 91
Batch 92
Batch 93
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Batch 94
Batch 95
Batch 96
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Batch 97
Batch 98
Batch 99
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Batch 100
Batch 101
Batch 102
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Batch 103
Batch 104
Batch 105
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Batch 106
Batch 107
Batch 108
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Batch 109
Batch 110
Batch 111
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Batch 112
Batch 113
Batch 114
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Batch 115
Batch 116
Batch 117
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Batch 118
Batch 119
Batch 120
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Batch 121
Batch 122
Batch 123
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Batch 124
Batch 125
Batch 126
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Batch 127
Batch 128
Batch 129
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Batch 130
Batch 131
Batch 132
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Batch 133
Batch 134
Batch 135
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Batch 136
Batch 137
Batch 138
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Batch 139
Batch 140
Batch 141
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Batch 142
Batch 143
Batch 144
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Batch 145
Batch 146
Batch 147
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Batch 148
Batch 149
Batch 150
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Batch 151
Batch 152
Batch 153
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Batch 154
Batch 155
Batch 156
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Batch 157
Batch 158
Batch 159
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Batch 160
Batch 161
Batch 162
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Batch 163
Batch 164
Batch 165
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Batch 166
Batch 167
Batch 168
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Batch 169
Batch 170
Batch 171
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Batch 172
Batch 173
Batch 174
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Batch 175
Batch 176
Batch 177
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Batch 178
Batch 179
Batch 180
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Batch 181
Last batch size unmatched...but may be fine!
End of data
Simulation for Test set took 138713.045316 seconds.
In [177]:
pv_history_list = result_list[0]
temp_pv_list = [1000]
temp_pv_list.extend(pv_history_list)
pv_history_list = temp_pv_list
plt.figure(figsize=(6,4))
test_phase_data['Trade Price'].plot()
plt.figure(figsize=(6,4))
plt.plot(pv_history_list, label='Chimp')
monkey_x = np.arange(len(pv_history_list))
monkey_y = ((1542.635 - 1000)/ len(pv_history_list)) * monkey_x + 1000
plt.plot(monkey_x, monkey_y, label='Monkey')
pt_x = np.arange(len(pv_history_list))
pt_y = ((2399.255 - 1000)/ len(pv_history_list)) * monkey_x + 1000
plt.plot(pt_x, pt_y, label='Patient Trader')
plt.legend()
Out[177]:
<matplotlib.legend.Legend at 0x7fd05d517150>
In [187]:
print(inverse_percentile(monkey_test.pv_history_list, 2206.8424410000021))
0.89706
Seems like our refinement has beaten 89.7 percent of the Monkeys.
Let's look at the equivalent annual ROI:
$$ ROI = (1 + r)^{1260/252} = 2.2068 $$$$ \Longrightarrow r = 0.1715278 \approx 17.15\% $$The number of iterations required for the Q-table to converge is tightly related to the number of valid actions and the discount factor. We set our discount factor $\gamma = 0.75$, and with two possible valid actions, any rewards that happen 10 days from the day of interest will be discounted to less than 5%. This means exploring all the possible actions would require roughly $2^{10}$ of iterations (given that we have only two valid actions). Therefore, 5000 iterations as what we have done earlier should guarantee a good convergence.
The result shows that our Chimp performs better than 89.7% of the Monkeys, which has not yet achieved statistical significance but seems to be a good start. For our trading bot to be useful, we need to test it against more stocks and make it outperform the PT in general. Due to that lack of resources, we won't cover that is this report.
This is a really interesting and challenging project for me for a few reasons. First is that I wasn't really familiar with time series data, and second is that I've never bought any stocks and had zero knowledge of the stock market whatsoever.
I started out using only supervised learning, and my first submit (which was like three months ago) wasn't very successful. I was then advised by my reviewer to try out some time series specific techiques such as ARIMA, which I did and failed, and reinforcement learning, which is what I'm using now. And though it hasn't achieved the level for practical use, I feel that this is the right way to go. About one month I after I started going with this approach, I was actually contacted on LinkedIn by the CEO of a Fintech sponsored hedge fund. And I realized they were actually doing something really similar, only that they were doing it with deep learning. This makes me feel more confident about this approach. I really want to thank my first reviewer for leading me to this path!
Following are some of the words of my reflection on my first submit:
There were quite a few places that I found puzzled and difficult.
First is the benchmark. I had no idea what a reasonable benchmark should be. How precise the prediction need to be? How far into the future do I want to predict? And can I predict that with the data?
The second is working with time series data. It's my first time working with time series data. The "physics" behind the scene is dynamic and time-dependent. How do I convert this data into something I can work with traditional machine learning methods, without losing information and constrains?
Third comes to model building. Should we build one model to predict for all the stocks? Or should we build one for each? If I build each of them independently, how do I incorporate sector information?
There are a lot more than what I've listed here, but these are the ones that came to mind first and were definitely among the hardest. However, though the word difficulty is used here, never for a second did I think any of them was difficult. Now that I think back, I think it's because I didn't know what would a reasonable goal be so there was not much pressure. The only thing that kept driving me forward was how to improve it, how to make it better. All of these questions are not so easy to answer, but my ignorance definitely lent me a hand this time.
It's intersting to look back on what I felt three months ago. A lot of things was really fresh an new to me back then but now it all feels quite natural to me. I really like this project. It got me into trading, and has made me more interested in reinforcement learning.
Try out a different feature set—we basically hand-picked our features in the hope that they could capture the patterns of the stock market. Our selection was based on volume price analysis but it may very well not be a good representation of what good VPA pracitioners are really doing. So one way to do this is to include more raw features (say we use tick data to the minute, and trace back more days) and then use PCA or an autoencoder to compress all that information. We can then use RFE or other feature selection methods to pick the better ones.
Feature discretization my not ideal—since the feature space is vast, one way or the other we are only going to cover a fraction of the space. As such, discretizing it really won't give us any benefits. In doing so we're actually losing a lot of information.
Use other data—we may also include economic data and social data so the trading bot can capture more than just what VPA method can capture.
Try out different parameters on reinforcement learning—the best trading stratege is that we make every order placement counts. To achieve this we can increase the discount factor and the trading cost.
Try out different algorithms on supervised learning—yes, I'm talking about deep learning!
Content source: Amarchuk/Stock-Price-Forecaster
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