# Granger Causality / VAR / Negative Correlations

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!

• The questions are a bit confusing as they stand. Constant refers to probably adding a constant to the regression, which should be standard, unless you expect that the theoretical relationship justifies no constant. VAR takes into account multiple time series simultaneously and the Pearson correlation is more or less useless between two time series; however, you can use the causality test regarding of their drift as causality test takes the differenced series into account. Commented Jun 25, 2015 at 20:24
• Okay, thank you! "you can use the causality test regarding of their drift as causality test takes the differenced series into account.". That's what I thought and understood, just wanted to check. "Pearson correlation is more or less useless between two time series". Could you explain that one?
– user80716
Commented Jun 26, 2015 at 8:27
• It's spurious correlation. Perhaps that's why I thought it may be strangely asked in the first place. Commented Jun 26, 2015 at 9:23
• two time series that are stationary and cointegrated is a contradiction. If the two series are stationary, they cannot be cointegrated. If they are cointegrated, they must be integrated (and thus nonstationary). One graph goes up, while the other goes down. Is it still valid and useful to test for Granger causality in such a case? Yes; the effect of one series on the other may be negative, for example. Commented Aug 4, 2015 at 16:49