I understand how PCA works, as I practiced it in order to understand the ranking of some objects with respect to some variables. My question is about the extension of the PCA to the analysis of time series of correlated variables.
Having a look at Can PCA be applied for time series data?, I did some research about what is called Singular Spectrum Analysis (SSA), and more specifically Multivariate - SSA (M-SSA).
This is basically what I understood from all of that. Taking for example a set of P variables, observed on N different objects. The classical PCA allows you to extract through the first eigen vectors of the covariance matrix which one of the P variables are actually relevent to represent your set of N different objects.
Using SSA (or M-SSA) for time series of P variables, you replace the N "objects" by (N ?) lagged versions of your time series in order to extract through the first eigen vectors of P characteristic signals (of the length of the time serie) that represent most of you variable time series.
My question if the following : what kind of information do I extract if I replace directly the "N objects" by the time series ? Meaning that every observation would be on "object". In that case, I can apply directly a "classical PCA" which will give me eigen vectors of length P. What can of result is this ?
For example, does the coefficients associated with the P vairables, of the first eigen vector, tell me how much these variables are relevant to the study of these time series ?
I hope I could make it clear ...