I have a dataset which contains multivariate time series and I would try applying PCA on it, but I'm not sure how to do it.
Consider the following scenario - you are monitoring N parameters of some machine during some time (M samples) and you save this test as an observation. You have Q such tests and you would like to learn something about the behaviour of these machines. But you want to reduce dimensionality first since there is Q time series with N parameters with M samples for each parameter.
How should I do PCA in this case?
My first approach:
- Take one test (N parameters, M samples)
Create samples in the following way
(p1t1, p2t1, ... pNt1)
(p1t2, p2t2, ... pNt2)
. . .
(p1tM, p2tM, ... pNtM)
Perform PCA on such dataset
And this resulted in getting principle components which basically gave me an answer which of the N parameters are the most important.
But what confuses me - I've done this only for a single test, how to do it for the whole dataset? Would it make sense to extend my approach and just add samples from other time series in the dataset, and then run PCA on all of that?
Another question is - is this a good approach for time series, to split series values into independent samples? Since they may depend on time. I read about time series stationarity, but this seems appropriate in case of domains such as stocks and similar, where there are things like trends and similar. These are just measurements of machine work during some time. Is this approach ok for that?
Any help is greatly appreciated, I'm very confused at the moment.