I've found all sorts of papers on dimension reduction for time series such as this (which doesn't seem to work anymore) and this.
All the papers seem to start with a discussion about how their method is superior to some other simpler method.
I have never had to think about dimension reduction in time series before so I am not familiar with any of the methods. So I got to thinking about what the simplest approach would be.

Objective: To arrive at a VARMA description of some multivariate time series data, whilst avoiding the need to estimate a huge number of variables with a small amount of data. Ultimately I want to end up with a VARMA equation in full dimension. My immediate problem is actually only a VMA(1) model though so if you know of something that only works for a VMA(1) model, then that is fine.

Is anything like the following method possible:

  1. Use principal Components Analysis (PCA) to reduce the dimension of the original data

  2. Fit a VARMA model on the most significant components of the transformed data

  3. Somehow use the rotation matrix from the PCA to convert the estimated time series parameters from the rotated space back to the original space.

I have found some info on structural specifications like scalar component models (SCMs) but this doesn't really reduce the dimension as much as PCA would, and quite frankly, SCM is really difficult to understand!

  • 1
    $\begingroup$ Dynamic factor models could be an alternative. There are a few different versions of them out there. Some of them could be viewed as approximately a PCA for time series data. $\endgroup$ – Richard Hardy Mar 20 '17 at 13:32
  • $\begingroup$ In practice (think HVAC industry) the thing they all do first is trim down to the fewest meaningful significant digits. Temperatures get truncated at tenths or hundredths of a degree. The second thing they do is throw away values where the measurement doesn't change, or doesn't change enough. The first looks for a different measure. The second looks for a different measure relative to the last stored measure (not row-to-row) to be larger than a technically significant magnitude before retaining. $\endgroup$ – EngrStudent - Reinstate Monica Oct 23 '18 at 15:25

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