I'm curious whether something I tried makes sense statistically...
I took a pile of time series inputs and performed an SVD. I want to predict variable Y on the basis of its own time series, and the first 50
SVD$u factors as external regressors.
It looked like an ARIMA(2,2,2) was a good fit for my variable Y with external regressors from the SVDu terms. Now, to forecast it on the basis of a path of the SVD...
To project the factors, I used a
SVD\$u because it was convenient. But was this foolish? Since the u values are orthogonal by construction, there should be no multivariate correlation, and this should deliver me a random walk, right? Or should I expect spurious correlation that will mess everything up, and that I should project each component of svd$u independently? I hesitate to do the latter because I like the way VAR() conveniently returns standard errors.