I am currently trying to reduce the number of variables I input into a vector autoregressive (VAR) model. For those that don't already know, VAR models are used on time-series data. My primary concern in regards to using PCA for dimensionality reduction in this scenario is that my time-series variables mainly consist of low-frequency power. This may end up being problematic given that--although the high-frequency components of my signals make up a minor portion of the total signal variance--those components may, indeed, be essential in terms of their granger causal impact on other variables. In short, I am worried that running PCA on my data will bias my model towards looking at only low-frequency signal interactions.

To address my concern, I would like to compare how different the PCA representations of my data are when the data is high-pass filtered vs. low-pass filtered. If the representations are similar enough, I will move forward with my current plan of running PCA on my data. Thus, my question is--what is the best way to compare PCA representations? Should I compare angles between eigenvectors? Should I remove the PCA aspect altogether for this and simply compare covariance matrices? Please advise.


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