Strange outcome of granger causality testing

Question

Hi here is the two time series that I want to test for whether the orange time series is granger causality of blue time series. As we can see that before the peak of blue time series, it is. On the contrary, after the peak of blue time series, it is not. But the granger testing outcome said that I need to reject the null hypothesis (no granger causality), thus orange time series is the granger causality of blue time series. But it's not what I observed from the figure. Is this because the two time series is not stationary and I need to make them stationary at first and then do the granger testing?

Any answer would be great appreciated, thank you!

Answer 1

I'm not sure how stationarity would play into this, but here's one broad idea of what's going on. Two time series can both Granger cause each other. This seems to be the case from your image. Orange causes blue to rise, and blue causes orange to fall.

Think about it in terms of the model. With just past values of the orange data, we couldn't predict when the orange series would start falling. That is, the coefficients of orange should be positive at time=2200, but negative at time=2600. The model will pick error-minimizing coefficients that won't be strongly negative, and thus won't help us predict when orange starts falling.

If you add in lags of blue, you can make a better prediction. Your model could say the current value of orange is proportional to the value of blue 200 time-steps ago. Then at time=2200, the value of blue at time=2000 starts to fall, and the model will correctly tell us that the value of orange should also start to fall. Since we got a better prediction when we add in lags of blue, we can say that blue Granger-causes orange.

Hope this helps!