By Evgenia "Jenny" Nitishinskaya, Maxwell Margenot, and Delaney Granizo-Mackenzie.
Part of the Quantopian Lecture Series:
Notebook released under the Creative Commons Attribution 4.0 License.
Representing data graphically can be incredibly useful for learning how the data behaves and seeing potential structure or flaws. Care should be taken, as humans are incredibly good at seeing only evidence that confirms our beliefs, and visual data lends itself well to that. Plots are good to use when formulating a hypothesis, but should not be used to test a hypothesis.
We will go over some common plots here.
In [1]:
# Import our libraries
# This is for numerical processing
import numpy as np
# This is the library most commonly used for plotting in Python.
# Notice how we import it 'as' plt, this enables us to type plt
# rather than the full string every time.
import matplotlib.pyplot as plt
If we're going to plot data we need some data to plot. We'll get the pricing data of Apple (AAPL) and Microsoft (MSFT) to use in our examples.
Knowing the structure of your data is very important. Normally you'll have to do a ton work molding your data into the form you need for testing. Quantopian has done a lot of cleaning on the data, but you still need to put it into the right shapes and formats for your purposes.
In this case the data will be returned as a pandas dataframe object. The rows are timestamps, and the columns are the two assets, AAPL and MSFT.
In [2]:
start = '2014-01-01'
end = '2015-01-01'
data = get_pricing(['AAPL', 'MSFT'], fields='price', start_date=start, end_date=end)
data.head()
Out[2]:
Indexing into the data with data['AAPL'] will yield an error because the type of the columns are equity objects and not simple strings. Let's change that using this little piece of Python code. Don't worry about understanding it right now, unless you do, in which case congratulations.
In [3]:
data.columns = [e.symbol for e in data.columns]
data.head()
Out[3]:
Much nicer, now we can index. Indexing into the 2D dataframe will give us a 1D series object. The index for the series is timestamps, the value upon index is a price. Similar to an array except instead of integer indecies it's times.
In [4]:
data['MSFT'].head()
Out[4]:
A histogram is a visualization of how frequent different values of data are. By displaying a frequency distribution using bars, it lets us quickly see where most of the observations are clustered. The height of each bar represents the number of observations that lie in each interval. You can think of a histogram as an empirical and discrete Propoability Density Function (PDF).
In [5]:
# Plot a histogram using 20 bins
plt.hist(data['MSFT'], bins=20)
plt.xlabel('Price')
plt.ylabel('Number of Days Observed')
plt.title('Frequency Distribution of MSFT Prices, 2014');
In finance rarely will we look at the distribution of prices. The reason for this is that prices are non-stationary and move around a lot. For more info on non-stationarity please see this lecture. Instead we will use daily returns. Let's try that now.
In [6]:
# Remove the first element because percent change from nothing to something is NaN
R = data['MSFT'].pct_change()[1:]
# Plot a histogram using 20 bins
plt.hist(R, bins=20)
plt.xlabel('Return')
plt.ylabel('Number of Days Observed')
plt.title('Frequency Distribution of MSFT Returns, 2014');
An alternative way to display the data would be using a cumulative distribution function, in which the height of a bar represents the number of observations that lie in that bin or in one of the previous ones. This graph is always nondecreasing since you cannot have a negative number of observations. The choice of graph depends on the information you are interested in.
In [7]:
# Remove the first element because percent change from nothing to something is NaN
R = data['MSFT'].pct_change()[1:]
# Plot a histogram using 20 bins
plt.hist(R, bins=20, cumulative=True)
plt.xlabel('Return')
plt.ylabel('Number of Days Observed')
plt.title('Cumulative Distribution of MSFT Returns, 2014');
A scatter plot is useful for visualizing the relationship between two data sets. We use two data sets which have some sort of correspondence, such as the date on which the measurement was taken. Each point represents two corresponding values from the two data sets. However, we don't plot the date that the measurements were taken on.
In [8]:
plt.scatter(data['MSFT'], data['AAPL'])
plt.xlabel('MSFT')
plt.ylabel('AAPL')
plt.title('Daily Prices in 2014');
In [9]:
R_msft = data['MSFT'].pct_change()[1:]
R_aapl = data['AAPL'].pct_change()[1:]
plt.scatter(R_msft, R_aapl)
plt.xlabel('MSFT')
plt.ylabel('AAPL')
plt.title('Daily Returns in 2014');
A line graph can be used when we want to track the development of the y value as the x value changes. For instance, when we are plotting the price of a stock, showing it as a line graph instead of just plotting the data points makes it easier to follow the price over time. This necessarily involves "connecting the dots" between the data points, which can mask out changes that happened between the time we took measurements.
In [10]:
plt.plot(data['MSFT'])
plt.plot(data['AAPL'])
plt.ylabel('Price')
plt.legend(['MSFT', 'AAPL']);
In [11]:
# Remove the first element because percent change from nothing to something is NaN
R = data['MSFT'].pct_change()[1:]
plt.plot(R)
plt.ylabel('Return')
plt.title('MSFT Returns');
Again, whenever using plots to visualize data, do not assume you can test a hypothesis by looking at a graph. Also do not assume that because a distribution or trend used to be true, it is still true. In general much more sophisticated and careful validation is required to test whether models hold, plots are mainly useful when initially deciding how your models should work.
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