I have a time-series dataset and I am a bit lost how to perform the analysis.
I have an dedependent variable and about 2000 independent variables for some entity over a time period of about 2500 daily observations (like daily consume behavior of an individual over time for 2000 products). In fact, those 2000 variables loosely "belong together". To be precise: Each of the 2000 variables can be assigned to one of three "main categories" (e.g., 600 variables belong to main category 1, 1200 belong to main category 2 and 200 to main category 3). Also, the variables belonging to one category are in most cases moderately to highly correlated.
Obviously, it won't make much sense to run a regression with 2000 independent variables. It is completely fine for my purpose to obtain just one coefficient for each "main category variable" (so three coefficients instead of 2000) in the end. However, I am unaware of techniques to "condense" my variables in three main variables before performing the final regressions. I cannot simply eliminate single variables from the setup to reduce the regressors and, for instance, choose only a subset of "most useful" variables.
Any ideas how to handle this problem?