granger_causality (pyleoclim.utils.causality.granger_causality)

pyleoclim.utils.causality.granger_causality(y1, y2, maxlag=1, addconst=True, verbose=True)[source]

statsmodels granger causality tests

Four tests for granger non causality of 2 time series.

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.

Wrapper for the functions described in statsmodel (https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.grangercausalitytests.html)

Parameters

  • y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed

  • y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed

  • maxlag (int or int iterable, optional) – If an integer, computes the test for all lags up to maxlag. If an iterable, computes the tests only for the lags in maxlag.

  • addconst (bool, optional) – Include a constant in the model.

  • verbose (bool, optional) – Print results

Returns

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 test statistic, 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.

Return type

dict

Notes

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

See also

pyleoclim.utils.causality.liang_causality

information flow estimated using the Liang algorithm

References

Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.

Granger, C. W. J. (1980). Testing for causality: A personal viewpoont. Journal of Economic Dynamics and Control, 2, 329-352.

Granger, C. W. J. (1988). Some recent development in a concept of causality. Journal of Econometrics, 39(1-2), 199-211.