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I am using PCA to reduce dimensionality prior to fitting a multivariate time-series dataset to a VAR (vector autoregressive) model. Is there any way to convert a PCA-derived VAR model to a full dimensional representation if I remove some principle components from the data prior to modeling? I know there is at least one way to convert a PCA-derived model to a model of the original data via backprojection (http://scot-dev.github.io/scot-doc/vartransform.html#covbivar1), but it seems like this might be impossible (or at least not recommended) if one were to remove some variance (principle components) from the dataset. The end goal is to investigate how the original variables interact with each other in terms of the ("full dimensional") model coefficients.

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