# Interpreting Granger causality test's results – i.e. $X = f(Y)$

The following is generated using http://www.wessa.net/rwasp_grangercausality.wasp:

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


My interpretation is that:

(i) Granger Causality Test: Y = f(X) p-value = 2.94360540545316e-05
The p-value is very small, thus the null hypothesis Y = f(X), X Granger causes Y, is rejected.

(ii) Granger Causality Test: X = f(Y) p-value = 0.760632773377753
The p-value is near to 1 (i.e. 76%), therefore the null hypothesis X = f(Y), Y Granger causes X, cannot be rejected.

Is my interpretation correct?

[Related to full question in Interpreting Granger causality test's results.]

no. the null hypothesis would be: X does not granger cause Y or the other way. Also, you accept or reject your null hypothesis depending on the level of significance.

if P value < Significance level, then Null hypothesis would be rejected.

if P value > Significance level, then Null hypothesis cannot be rejected.

For your specific example, as you are using F test the rejection of null hypothesis will be done as follows:

Compare obtained F_value to the F_critical, If F_value is greater than F_critical then you can reject the null hypothesis but before that you have to check P_value also. If P_value is less than Significance level (5% widely used) then only you can reject your null hypothesis.

• Can you clarify why you think checking the $p$-value and the $F$-value will lead to different conclusions? As it stands your answer is misleading. Oct 5, 2017 at 10:58