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i have a vector of time series data (1020x30; an index of neural activation measured at 1020 timepoints in 30 participants). I also have assessed 5 covariates of interest at a group level (eg age). I want to estimate how much those factors contribute to neural activation across time. I could estimate an ols at each time point, of course. However, what would be the best way to correct for multiple comparisons? Make a null distribution at each time point by randomly shuffling matrices? Every help would be very much appreciated!

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I read a paper a while back that used an L2-norm to do sort of a "temporal smoothing" process across the predictions, which I thought was an interesting way to deal with time-varying components. I unfortunately can't find it but here's a similar paper I found

Learning Time-Varying Graphs using Temporally Smoothed L1-Regularized Logistic Regression http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.480.550&rep=rep1&type=pdf

I don't think this answers the question directly, but perhaps it can give you ideas of how to play around with penalty functions across the time points, to get a "stable" estimate of each factor's contribution to the neural activation?

On the other hand, going back to your proposed idea of shuffling and permuting the values/matrices to determine each factor's estimate, then here's a page that talks about how this same procedure is done in random forests.

Hope this helps!

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