Python library for cointegration analysis.

• Carry out cointegration test
• Evaluate spread between cointegrated time-series
• Generate cointegrated time-series artificially
• Based on scikit-learn API

$ pip install cointanalysis

See Hamilton's book.

Let us see how the main class CointAnalysis works using two ETFs, HYG and BKLN, as examples. Since they are both connected with liabilities of low-rated companies, these prices behave quite similarly.

The method test carries out a cointegration test. The following code gives p-value for null-hypothesis that there is no cointegration.

from cointanalysis import CointAnalysis

hyg = ...   # Fetch historical price of high-yield bond ETF
bkln = ...  # Fetch historical price of bank loan ETF
X = np.array([hyg, bkln]).T

coint = CointAnalysis()
coint.test(X)

coint.pvalue_
# 0.0055

The test has rejected the null-hypothesis by the p-value of 0.55%, which implies cointegration.

The method fit finds the cointegration equation.

coint = CointAnalysis().fit(X)

coint.coef_
# np.array([-0.18  1.])
coint.mean_
# 6.97
coint.std_
# 0.15

This means that spread "-0.18 HYG + BKLN" has a mean 6.97 and a standard deviation of 0.15.

In fact, the prices adjusted with these parameters clarifies the similarities of these ETFs:

The time-series of spread is obtained by applying the method transform subsequently. The mean and the standard deviation are automatically adjusted (unless you pass parameters asking not to).

spread = coint.transform(X)
# returns (-0.18 * hyg + 1. * bkln - 7.00) / 0.15

spread = coint.transform(X, adjust_mean=False, adjust_std=False)
# returns -0.18 * hyg + 1. * bkln

The method fit_transform carries out fit and transform at once.

spread = coint.fit_transform(X)

The result looks like this:

• statsmodels

• J. D. Hamilton, "Time Series Analysis", (1994).