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I have a time series of different physical measurements. One of these, lets call it X, is determined by the others, $Y_1$...$Y_n$, through various physical processes (which are complex and not fully known). There is no influence of X on Y. The Y parameters are all caused by the same source, so they are correlated to various degrees. Some of these correlations are close to 1 or -1.

I am looking for a statistical method to analyze the impact of the different parameters on X.

PCA was suggested, but I have not used it before and from what I read it seems not well suited to the problem because of the correlation between the input parameters.

It might be possible to reduce the Ys to a combined parameter for each physical process (where correlation is lowest between them) and then use PCA, but I would be interested if there is a statistical method better suited to my problem, where I can use all parameters. Maybe someone here has an idea?

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  • $\begingroup$ You should apply PCA on Y, and then check correlation of different factors to X. $\endgroup$
    – Arun Jose
    Oct 19, 2016 at 6:59
  • $\begingroup$ Thats a good point actually, thanks. Maybe I should do this with all subsets of parameters that relate to the same physical process. $\endgroup$ Oct 19, 2016 at 8:45

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ARIMAX Here is a case where it has been used: https://forecasters.org/wp-content/uploads/gravity_forms/7-2a51b93047891f1ec3608bdbd77ca58d/2013/07/Kongcharoen_Chaleampong_ISF2013.pdf

And there has been a discussion here, on how to do it in R: How to fit an ARIMAX-model with R?

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  • $\begingroup$ Your reference showed no concern given to detecting and incorporating unknown deterministic structure causing pulses/level shifts/local time trends or seasonal pules OR possible changes in either error variance or parameters over time. Probably because they didn't have access to good tools. $\endgroup$
    – IrishStat
    Oct 19, 2016 at 13:16
  • $\begingroup$ True, when using ARMA-models, one needs to make the time series stationary. It is an art by itself and best results are often made by hand. Most automatic methods tend to give bad results. $\endgroup$ Oct 19, 2016 at 14:24
  • $\begingroup$ I agree that there has to be some intelligent/assumption checking device whether it be an experienced hand/mind or an advanced software agent OR both $\endgroup$
    – IrishStat
    Oct 19, 2016 at 14:35

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