We will download price data as in the previous recipe; but this time for a single stock. Again, we will calculate the log returns of the close price of this stock, and use that as an input for the normality test function.

This function returns a tuple containing a second element—a p-value between zero and one. The complete code for this tutorial is as follows:

import datetime
import numpy
from matplotlib import finance
from statsmodels.stats.adnorm import normal_ad
import sys

#1. Download price data

# 2011 to 2012
start = datetime.datetime(2011, 01, 01)
end = datetime.datetime(2012, 01, 01)

print "Retrieving data for", sys.argv[1]
quotes = finance.quotes_historical_yahoo(sys.argv[1], start, end, asobject=True)

close = numpy.array(quotes.close).astype(numpy.float)
print close.shape

print normal_ad(numpy.diff(numpy.log(close)))

The following shows the output of the script with p-value of 0.13:

Retrieving data for AAPL
(252,)
(0.57103805516803163, 0.13725944999430437)

This recipe demonstrated the Anderson Darling statistical test for normality, as found in scikits-statsmodels. We used the stock price data, which does not have a normal distribution, as input. For the data, we got a p-value of 0.13. Since probabilities range between zero and one, this confirms our hypothesis.