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> Eigendecomposition of the covariance matrix, essentially PCA, is probably the first non-trivial step in the analysis of any dataset

For a sufficiently narrow definition of "dataset", perhaps. I don't think it's the obvious step one when you want to start understanding a time series dataset, for example. (Fourier transform would be a more likely step two, after step one of actually look at some of your data.)



I agree, but: the technique of “singular spectrum analysis” is pretty much PCA applied to a covariance matrix resulting from time-lagging the original time series. (https://en.wikipedia.org/wiki/Singular_spectrum_analysis)

So this is not unheard of for time series analysis.


Exactly that's a good example!




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