I have two questions on Granger causality. I feel puzzled after reading a dozen of papers on the topic and it appears to me that I need to clarify my understanding of Granger causality.
Question 1 : Assuming we have a two time series that are stationary and cointegrated, is it then o.k. to apply this test: http://statsmodels.sourceforge.net/0.6.0/generated/statsmodels.tsa.stattools.grangercausalitytests.html ? What's the purpose of "addconst=True"?
Is this test a "VAR Granger causality test" or just a "Granger causality test"? Is it the same?
Question 2: Assuming we have timeseries A and timeseries B. Let's say the Pearson correlation of the two timeseries is negative. One graph goes up, while the other goes down. Is it still valid and useful to test for Granger causality in such a case? Given we find one-directional causality, does that still mean that the lagged value of A Granger-causes B? If yes, I guess I could control that effect with an Impulse Response Function.
Thank you!
Best Answer
Based on your own statements and comments your first question is not clear. But, your second one is perfectly clear. And, we can say unequivocally that Granger-causality is not limited to one direction (positive or negative). A variable can Granger-cause another one with a positive effect (the two variables are positively correlated) or a negative effect (the two variables are negatively correlated). That's perfectly ok. Granger-causality testing checks whether that variable adds information vs. just using an autoregressive model using only y t-1 as the independent variable.