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I have tested for Granger causality in my data and have the $p$-value related information such as,

$Granger Granger causality H0: general do not Granger-cause special

data: VAR object sims.2 F-Test = 3.2493, df1 = 2, df2 = 22, p-value = 0.04802

Is there any way I can visually depict the causality occurring between the two variables? Or anything hinting towards the presence of causality would be appreciated as well.

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If you are interested in a Yes/No answer (which is often the reason why people do hypothesis testing), there is not much to visualize. If, on the other hand, you are interested in the effect size and its lag structure, you can look at impulse-response functions and see what effect a shock to $X$ has on $Y$ over several periods.

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