I'm trying to educate myself on Granger Causality. I've read the posts on this site and several good articles online. 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?
- What key insights have I overlooked?
- Also what is the meaning and interpretation of the CCF charts? (I'm assuming CCF is cross correlation.)
Here are the results and plots that I have interpreted:
Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Herman Ole Andreas Wold' @ wold.wessa.net Granger Causality Test: Y = f(X) Model Res.DF Diff. DF F p-value Complete model 356 Reduced model 357 -1 17.9144959720894 2.94360540545316e-05 Granger Causality Test: X = f(Y) Model Res.DF Diff. DF F p-value Complete model 356 Reduced model 357 -1 0.0929541667364279 0.760632773377753
- Test was based upon 357 data points and was performed with a lag value of 1
- The p-value of 0.0000294 means I can reject the null hypothesis that x does not cause y for the Y = f(x).
- The p-value of .76 allows me to accept the null for X = f(Y)
- The fact that first hypothesis was rejected and second accepted is a good thing
- I'm a little rusty on my F-test so I don't really have anything to say on this for now.
- I'm also not sure how to interpret the CCF graph.
I really appreciate it if any of you who are well versed with Granger-causality could let me know if I'm interpeting this correctly and also fill in some of the blanks.
Thanks for your help.