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Sequential testing is common for Time series.

Think SupF kind of tests, or a chow-test for structural break in the parameters over a grid of data points. So, we have many (as many as data points modulo few points from the start and end) statistics, and their correspondent P-values.

FDR is good for the independent case, what I just described yields highly correlated test statistics, so the FDR is too restrictive. That is, a rejection is a clear sign for a break, but no-rejection.. might be because we have many data points (so FDR_pv is small), I can search over more coarse grid to reduce the number of tests, so a max over a grid = {1,2,3,...,T} may not be rejected but a max over a grid = {1,3,5,...,T} may be rejected, which does not make too much sense.

Is anyone familiar, and may be able to give some references for FDR extension to the Time Series domain?

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