This exercise notebook refers to this lecture. Please use the lecture for explanations and sample code.
https://www.quantopian.com/lectures#Spearman-Rank-Correlation
Part of the Quantopian Lecture Series:
In [1]:
import numpy as np
import pandas as pd
import scipy.stats as stats
import matplotlib.pyplot as plt
import math
In [2]:
n = 100
x = np.linspace(1, n, n)
y = x**5
#Your code goes here
corr = np.corrcoef(x, y)[1][0]
print corr
plt.plot(x, y);
In [3]:
#Your code goes here
xrank = stats.rankdata(x, method='average')
yrank = stats.rankdata(y, method='average')
diffs = xrank - yrank
spr_corr = 1 - 6*np.sum( diffs*diffs )/( n*( n**2 - 1 ) )
print "Because the ranks of the two data sets are perfectly correlated,\
the relationship between x and y has a Spearman rank correlation coefficient of", spr_corr
Check your results against scipy's Spearman rank function. stats.spearmanr
In [4]:
# Your code goes here
stats.spearmanr(x, y)
Out[4]:
In [5]:
n = 100
a = np.random.normal(0, 1, n)
#Your code goes here
b = [0] + list(a[:(n-1)])
results = stats.spearmanr(a, b)
print "Despite the underlying relationship being a perfect correlation,\
the one-step lag led to a Spearman rank correlation coefficient of\n", results.correlation, \
", meaning the test failed to detect the strong relationship."
In [6]:
n = 100
c = np.random.normal(0, 2, n)
#Your code goes here
d = 10*c**2 - c + 2
results = stats.spearmanr(c, d)
print "Despite an exact underlying relationship of d = 10c^2 - c + 2,\
the non-monotonic nature of the relationship led to a Spearman rank Correlation coefficient of", \
results.correlation, ", meaning the test failed to detect the relationship."
plt.scatter(c, d);
Here we'll define a simple momentum factor (model). To evaluate it we'd need to look at how its predictions correlate with future returns over many days. We'll start by just evaluating the Spearman rank correlation between our factor values and forward returns on just one day.
Compute the Spearman rank correlation between factor values and 10 trading day forward returns on 2015-1-2.
For help on the pipeline API, see this tutorial: https://www.quantopian.com/tutorials/pipeline
In [7]:
#Pipeline Setup
from quantopian.research import run_pipeline
from quantopian.pipeline import Pipeline
from quantopian.pipeline.data.builtin import USEquityPricing
from quantopian.pipeline.factors import CustomFactor, Returns, RollingLinearRegressionOfReturns
from quantopian.pipeline.classifiers.morningstar import Sector
from quantopian.pipeline.filters import QTradableStocksUS
from time import time
#MyFactor is our custom factor, based off of asset price momentum
class MyFactor(CustomFactor):
""" Momentum factor """
inputs = [USEquityPricing.close]
window_length = 60
def compute(self, today, assets, out, close):
out[:] = close[-1]/close[0]
universe = QTradableStocksUS()
pipe = Pipeline(
columns = {
'MyFactor' : MyFactor(mask=universe),
},
screen=universe
)
start_timer = time()
results = run_pipeline(pipe, '2015-01-01', '2015-06-01')
end_timer = time()
results.fillna(value=0);
print "Time to run pipeline %.2f secs" % (end_timer - start_timer)
my_factor = results['MyFactor']
In [8]:
n = len(my_factor)
asset_list = results.index.levels[1].unique()
prices_df = get_pricing(asset_list, start_date='2015-01-01', end_date='2016-01-01', fields='price')
# Compute 10-day forward returns, then shift the dataframe back by 10
forward_returns_df = prices_df.pct_change(10).shift(-10)
# The first trading day is actually 2015-1-2
single_day_factor_values = my_factor['2015-1-2']
# Because prices are indexed over the total time period, while the factor values dataframe
# has a dynamic universe that excludes hard to trade stocks, each day there may be assets in
# the returns dataframe that are not present in the factor values dataframe. We have to filter down
# as a result.
single_day_forward_returns = forward_returns_df.loc['2015-1-2'][single_day_factor_values.index]
#Your code goes here
r = stats.spearmanr(single_day_factor_values,
single_day_forward_returns)
print "A Spearman rank rorrelation test yielded a coefficient of %s" %(r.correlation)
Repeat the above correlation for the first 60 days in the dataframe as opposed to just a single day. You should get a time series of Spearman rank correlations. From this we can start getting a better sense of how the factor correlates with forward returns.
What we're driving towards is known as an information coefficient. This is a very common way of measuring how predictive a model is. All of this plus much more is automated in our open source alphalens library. In order to see alphalens in action you can check out these resources:
A basic tutorial: https://www.quantopian.com/tutorials/getting-started#lesson4
An in-depth lecture: https://www.quantopian.com/lectures/factor-analysis
In [9]:
rolling_corr = pd.Series(index=None, data=None)
#Your code goes here
for dt in prices_df.index[:60]:
# The first trading day is actually 2015-1-2
single_day_factor_values = my_factor[dt]
# Because prices are indexed over the total time period, while the factor values dataframe
# has a dynamic universe that excludes hard to trade stocks, each day there may be assets in
# the returns dataframe that are not present in the factor values dataframe. We have to filter down
# as a result.
single_day_forward_returns = forward_returns_df.loc[dt][single_day_factor_values.index]
rolling_corr[dt] = stats.spearmanr(single_day_factor_values,
single_day_forward_returns).correlation
In [10]:
# Your code goes here
print 'Spearman rank correlation mean: %s' %(np.mean(rolling_corr))
print 'Spearman rank correlation std: %s' %(np.std(rolling_corr))
plt.plot(rolling_corr);
Congratulations on completing the Spearman rank correlation exercises!
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