Defining cointegration

Cointegration is similar to correlation but is viewed by many as a superior metric to define the relatedness of two time series. Two time series x(t) and y(t) are cointegrated if a linear combination of them is stationary. In such a case, the following equation should be stationary:

y(t) – a x(t)

Consider a drunk man and his dog out on a walk. Correlation tells us whether they are going in the same direction. Cointegration tells us something about the distance over time between the man and his dog. We will show cointegration using randomly generated time series and real data. The Augmented Dickey-Fuller (ADF) test (see http://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test) tests for a unit root in a time series and can be used to determine the cointegration of time series.

For the following code, have a look at the cointegration.py file in this book's code bundle:

import statsmodels.api as sm
from pandas.stats.moments import rolling_window
import pandas as...