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Let's say we have two random variables a and b, which are correlated. Will their cumulative sums (A and B) be correlated too? I find it logical that corr(A,B) = corr(a,b). I am bit rusty in my statistics so I am not sure if this very trivial or I am missing something...

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  • $\begingroup$ if you calcuilatte cumulative sums, you are putting non-staionarity into your data series. The analogue would be what granger and newbold did when they constructed two random walks and regressed them on each other. Essentially, the variance of each series is constantly changing ( increasing because you have two random walks ) so any calculation ( such as auto-correlation ) is going to be flawed, statistically speaking. Since, a cumulative sum is a random walk with no variance, your two series would have a similar problem. So, the answer is: "Don't do that". $\endgroup$ Commented Sep 29, 2022 at 14:21
  • $\begingroup$ I see.. Thanks! $\endgroup$ Commented Sep 30, 2022 at 12:23

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