I have a multivariate time-series dataset, and would like to run PCA on my dataset to reduce the number of variables I input into a time-series model. I am concerned that running PCA may end up biasing my data towards low-frequency signal interactions given that most of the power in my signals lies in the lower frequency end (0-10 Hz). To get around this issue, I am wondering if it is possible to somehow weight the high frequency time-points of the signal to give them greater overall power, and reduce the likelihood that high-frequency signal interactions are washed out of my dataset after running PCA and retaining only a handful of principle components. Is there any way to do this reliably, or will I end up completely distorting the statistical properties of my original signal?

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    $\begingroup$ You can simply apply a frequency shaping filter to the original data, run PCA and apply the inverse filter on the PCA results. As long as the filter is invertible (minimum phase) and reasonably well behaved (no more than, say, 30dB boost or cut) that should work $\endgroup$ – Hilmar Oct 1 '18 at 15:42

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