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Is the Granger causality test results directionally correct?
I also came across a very helpful tool, the Bivariate Granger Causality – Free Statistics Calculator, that allows you to enter your time series and calculate the Granger Stats. Below, is the output from the sample data included on the site. I have also taken a crack at interpreting the results. Is my interpretation directionally correct?
How to run Granger test in Statsmodels?
I’ve constructed two data sets (sine functions shifted in time with noise added) and put them in a “data” matrix with signal 1 as the first column and signal 2 as the second. I then ran the tests using: granger_test_result = sm.tsa.stattools.grangercausalitytests(data, maxlag=40, verbose=True)`
How does the Granger test test the null hypothesis?
A nice blog about the granger test can be found here btw. and tests the NULL Hypothesis that X does NOT Granger cause Y, i.e. that the coefficients of the lags of X are not significant. The p-value you get comes from a Wald test. If it is lower than your significance level (in this case 0.05) you can reject the NULL, so X Granger causes Y.
How to find the optimal lag in Statsmodels?
I then ran the tests using: granger_test_result = sm.tsa.stattools.grangercausalitytests(data, maxlag=40, verbose=True)` The results showed that the optimal lag (in terms of the highest F test value) were for a lag of 1.
Is the time series of Granger causality stationary?
A plot of both time series (see Figure 2) shows that neither series is stationary. As a result, we will instead study the first differences of each time series. The data and time series plots for these are shown in Figures 3 and 4. The plots suggest that the time series may be stationary.
How are regressions used to test causality in economics?
Ordinarily, regressions reflect “mere” correlations, but Clive Granger argued that causality in economics could be tested for by measuring the ability to predict the future values of a time series using prior values of another time series.
Is the null hypothesis of no Granger causality rejected?
Then the null hypothesis of no Granger causality is not rejected if and only if no lagged values of an explanatory variable have been retained in the regression. In practice it may be found that neither variable Granger-causes the other, or that each of the two variables Granger-causes the other. Let y and x be stationary time series.