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I have the following results from a Granger test. Can someone tell me how to interpret them? I understand that p.val(ue) < 0.05 is significant for rejecting the null hypothesis. BUT do ftest or r2(squared) add any additional information?

A g-cause B
 ftest = 7.523583 p.val = 0.006165445 R2 = 0.005235041
 ftest = 5.535103 p.val = 0.004030749 R2 = 0.007986544
 ftest = 3.637428 p.val = 0.01242363  R2 = 0.008143064

B g-cause A
 ftest = 0.3040705 p.val = 0.5814277 R2 = 0.0002147836
 ftest = 0.5627182 p.val = 0.5697845 R2 = 0.0008759121
 ftest = 2.365794  p.val = 0.0693209 R2 = 0.005935409
sundancer
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    Our FAQ provides some advice. "Make it relevant to others" might be apt here: although the question is clear, it is utterly without context and therefore will be understood and followed only by a handful of expert, dedicated users who are able to guess what's really going on. With a little context, including a brief description of the data (and software) and a statement of your objectives, you can interest many more people who might be able to make a contribution. – whuber Jun 12 '12 at 12:07
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    Oh I see. Well, I thought this was a pure stats question. I have googled a million pages and I can't find paper that uses anything other than the p.value - seems a bit odd. – sundancer Jun 13 '12 at 08:17

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They are telling you the same information in different ways. Granger causality tests if the history of X is useful for forecasting Y over just using Y's history. Consider the regression:

\begin{align} Y_t = a_0 + a_1 Y_{t-1} + a_2 Y_{t-2} ... + b_1 X_{t-1} + b_2 X_{t-2} ... + e_t \end{align}

The granger causality tests the joint hypothesis $\vec{b} = 0.$ The F statistic is the test statistic used to get the p-value. The $R^2$ is the goodness of fit metric for the regression.

user253239
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