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I am still learning how to interpret the results of a Granger causality test.

Granger Causality Test: Y = f(X)
Model   Res.DF  Diff. DF    F   p-value
Complete model  1000            
Reduced model   1001    -1  9.98656377696739    0.00162424264659028

Granger Causality Test: X = f(Y)
Model   Res.DF  Diff. DF    F   p-value
Complete model  1000            
Reduced model   1001    -1  61.7745391599339    9.92054758804637e-15

My interpretation is that in both tests the null hypothesis is not rejected which means that both variables are likely to cause each other. Although the 2nd test is more likely to be casual because of the significantly smaller p-value. Can anyone please help me figure out if I am correct or incorrect?

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    $\begingroup$ Maybe casual should be causal?n Care to edit? $\endgroup$ Commented Oct 7, 2021 at 11:36

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P-values are very low in both cases, so $H_0$ of no Granger causality is rejected. That is, there seems to be Granger causality in both cases. The evidence is pretty strong in both cases.

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  • $\begingroup$ May i ask does the 2nd test say that it is likely that x granger causes y? or is it saying that it is likely that y granger causes x $\endgroup$ Commented Oct 6, 2021 at 18:52
  • $\begingroup$ @StrategicGamer, as far as I can tell, the second one is about $Y$ Granger-causing $X$. $\endgroup$ Commented Oct 6, 2021 at 19:44
  • $\begingroup$ Thank you. I'm still new to cross-validation. I just accepted your conclusion and ticked the mark. I appreciate your help. Your conclusion along with some of the research I've done since has really helped me become significantly more proficient in advanced data science. $\endgroup$ Commented Jun 21, 2022 at 20:18

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