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The answer to this question has probably been answered multiple times but I'm lacking the right keywords to find the answer.

I've tested on 24 time series Granger-causality from one series to the other (23 VARs, after checking stationarity and by using AIC minimization). I reject the null hypothesis of no Granger-causality at the 5% level on 4 series out of 23. My understanding is that: I should be finding 5%*23=1 false positive. I am finding 4 times that. Can I conclude there is evidence of Granger-causality? On what? From the series to the whole set?

Edit: to be very clear, I am interested in testing series 1 Granger-causes all other series. So I made 23 VARs of series 1 and each other series:

series 1 and series 2

series 1 and series 3

... Can I conclude there is statistical evidence series 1 Granger-causes the set?

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Your null hypothesis is that there is no Gragner-causality. You are finding that you reject the hypothesis on 4 of the 23 series. Note that the probability of rejecting, given the null hypothesis is true, is $0.05$. So rejecting 4 or more (incorporating more extreme events) out of the 23 series has probability becomes the value of the binomial distribution with $n=23$ and $p=0.05$: $$P(N_{rej}\geq 4) = 1- P(N_{rej} \leq 3) = 1- F_{Bin}(3)=1-\sum_{i=0}^3 \left(\begin{array}{c} 23 \\ i \end{array} \right) 0.05^i (1-0.05)^{23-i}$$ This is the probability of this event or a more extreme occurring. Depending on your significance threshold we either reject or do not reject the null hypothesis here.

Assuming you set your confidence level to 5\% we get $0.025815$ which means we reject the null hypothesis.

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