0
$\begingroup$

I am complete novice so bear with me. As per the documentation on statsmodels, the NULL hypothesis is that the second time series X2 does NOT granger cause X1.

Granger Causality
number of lags (no zero) 1
ssr based F test:         F=3.0976  , p=0.0792  , df_denom=369, df_num=1
ssr based chi2 test:   chi2=3.1227  , p=0.0772  , df=1
likelihood ratio test: chi2=3.1097  , p=0.0778  , df=1
parameter F test:         F=3.0976  , p=0.0792  , df_denom=369, df_num=1

Granger Causality
number of lags (no zero) 2
ssr based F test:         F=2.3378  , p=0.0980  , df_denom=366, df_num=2
ssr based chi2 test:   chi2=4.7394  , p=0.0935  , df=2
likelihood ratio test: chi2=4.7094  , p=0.0949  , df=2
parameter F test:         F=2.3378  , p=0.0980  , df_denom=366, df_num=2

After reading through all different articles, I am still confused to understand what to make out of the P-value and the level of significance.

$\endgroup$
0
$\begingroup$

The null hypothesis in the granger causality test is that the second time series does not Granger cause the first time series (column two and column one respectively for the module that you are using). In your case your p-values are larger than 0.05, which is the traditional cutoff for statistical significance. That is to say you fail to reject the null hypothesis. If you were to pick a different cutoff for statistical significance then that might alter your conclusion, but you would probably be met with a lot of skepticism for picking a different value (especially if it is less stringent; i.e., higher than 0.05).

Further reading: https://blog.minitab.com/blog/adventures-in-statistics-2/understanding-hypothesis-tests-significance-levels-alpha-and-p-values-in-statistics

TL/DR: The level of significance refers to what p-value you use as your cutoff between failing to reject and rejecting the null hypothesis. The by far most commonly accepted choice is 0.05

$\endgroup$
  • $\begingroup$ so, just so that I understand, in my case I am saying that the second time series in fact does cause the first one, is that correct? $\endgroup$ – user92636 Oct 9 at 19:44
  • $\begingroup$ It is saying that you do not have sufficient evidence to say that the second time series causes the first. So the answer to your question at the risk of using sloppy language is no. The null hypothesis is that the second series does NOT cause the first and you have failed to reject that hypothesis. So you have insufficient evidence to say that the second causes the first. $\endgroup$ – Patrick Oct 9 at 20:48
  • $\begingroup$ thank you for the answer, but if I increase the lags to 4, then the last two lags will give me a p value which is much smaller than 0.05, so then should reject the null based on the first two lags or fail to reject the null? $\endgroup$ – user92636 Oct 10 at 16:01
  • $\begingroup$ You would then reject the null hypothesis because you have found lags that are statistically significant. The thing that is unclear to me about the package that you chose is if it offers any adjustment/correction for multiple comparisons: en.wikipedia.org/wiki/Multiple_comparisons_problem So I would be sure that indeed you have p-values that are much smaller than 0.05/(#of lags) to avoid this problem. That is to say make sure your p-values are below 0.05/4. $\endgroup$ – Patrick Oct 14 at 13:26

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.