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I have 1000 financial time series (closing prices), I am using Toda-Yamamoto test. It is impossible to calculate the causality manually as there are $C_{1000}^{2-1000}$ cases.

Is there a way in which I could calculate the causality mutually?

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  • $\begingroup$ The original question is (with a minor tweak) okay, the update places it more clearly off topic. I have edited to remove that addition. The updated question would belong elsewhere but the original question was asked-and-answered and should not have been changed after it was answered.. $\endgroup$ – Glen_b May 6 '17 at 7:49
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If you want to test for Granger causality of each pair, both ways ($x \rightarrow y$ and $y \rightarrow x$), you can do it in a nested loop. Let a pair of series be indexed $(i,j)$. The outer loop would be over $i$ from 1 to 1000; the inner loop would be over $j$ from 1 to 1000; and you would skip cases where $i=j$. That would exhaust all pairs $(i,j)$ and would test the causality both ways.

However, is that what you want? If all the pairs of the 1000 series were actually Granger-causal both ways (as is under the null hypothesis), you would on average reject Granger causality in 5% of the tested cases for a significance level of 5% (or 1% for 1%, or similar). There would be a lot of false positives.

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  • $\begingroup$ thank you @Richard but in looping it's taking too much time. I want some quick way to calculate the result means the computation time should be less then 30 sec. $\endgroup$ – john Dec 29 '15 at 9:37
  • $\begingroup$ Since the question seems to concern programming and computational efficiency rather than statistics, it could better suit Stack Overflow than Cross Validated. $\endgroup$ – Richard Hardy Dec 29 '15 at 9:40

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