statsmodels.tsa.stattools.grangercausalitytests(x, maxlag, addconst=True, verbose=True)[source]

four tests for granger non causality of 2 timeseries

all four tests give similar results params_ftest and ssr_ftest are equivalent based on F test which is identical to lmtest:grangertest in R

xarray, 2d

data for test whether the time series in the second column Granger causes the time series in the first column


the Granger causality test results are calculated for all lags up to maxlag


print results if true


all test results, dictionary keys are the number of lags. For each lag the values are a tuple, with the first element a dictionary with teststatistic, pvalues, degrees of freedom, the second element are the OLS estimation results for the restricted model, the unrestricted model and the restriction (contrast) matrix for the parameter f_test.


TODO: convert to class and attach results properly

The Null hypothesis for grangercausalitytests is that the time series in the second column, x2, does NOT Granger cause the time series in the first column, x1. Grange causality means that past values of x2 have a statistically significant effect on the current value of x1, taking past values of x1 into account as regressors. We reject the null hypothesis that x2 does not Granger cause x1 if the pvalues are below a desired size of the test.

The null hypothesis for all four test is that the coefficients corresponding to past values of the second time series are zero.

‘params_ftest’, ‘ssr_ftest’ are based on F distribution

‘ssr_chi2test’, ‘lrtest’ are based on chi-square distribution

References Greene: Econometric Analysis