I'm looking for some advice on selecting an appropriate forecasting model for panel data. I'm just starting out in the field and would appreciate any hints or rules of thumb to help make such decisions. Here's my particular case:
I have quarterly data on the incomes of 12 competing companies. Each company has three main sources of income: A,B,C (same for all of them). For each source and company, I have data starting from about 2010, so about 30 time points. The data is non-stationary. I think this kind of structure is called 'panel data'. I want to make forecasts for each company and source one time period ahead.
Additionally, it is predicted that the incomes depend on a set of market parameters. A set of 50 time series ("drivers", mostly various stock exchange indices etc.) is proposed, this data is freely available. Each of these 50 series falls into one of 10 categories
My questions are the following:
The proposed set of potential drivers is too large. Before running any regression for the incomes, I want to reduce it to a more manageable amount. Is this reasonable? If yes, which method should I choose? I read about various dimension reduction procedures, but I don't really have any experience which would allow me to make a decision. Ideally I'd like something with a ready made R library, for example DFA - does this make sense in this context (nonstationarity, potential other irregularities).
Suppose I managed to separate out several drivers using some dimension reduction technique. How would I structure my model now? Should I consider three separate models for A, B, C? It seems like I would lose something in doing that because the income sources are likely correlated. I thought about using a dynamic panel model (plm supports this). But the data isn't stationary, perhaps there are models that don't require this? Another thing is seasonality, since the data is quarterly it would make sense to account for this somehow - nowcasting?). I have zero knowledge about (dynamic) panel data models so I'd be grateful for any pointers.
Does it make sense to separate the procedure in two steps (dimension reduction and fitting a panel model)? Does it potentially introduce many errors? Can and should the two steps be combined somehow? Are there perhaps more natural approaches to modelling such financial panel data? With so few data points I don't think it's sensible to model each company/source separately, I read that panel analysis has the advantage of not requiring many time points.
Edit: Here's what the data is structured like for clarity (not the real data, just generated random numbers in Excel). On top of this I have access to an external set of ~50 time series which would serve as potential predictors which can be classified into ~10 categories.
Edit 2: In response to DJohnson's wonderful answer, I have a few more questions:
MANOVA and CCA approaches are suggested once the relevant predictors are uncovered. I'm curious on how to modify these procedures to accommodate time series data. In other words, what is the procedure to go from an "ordinary" model to a time-sensitive one? How would the equations for the two proposed models change? Besides, I don't quite get why nominally ordered time would be appropriate.
Going back to dimensionality reduction and predictor selection: I forgot to mention something relevant in my original question, I edited it in now, namely that each of the potential 50 predictors falls into one of 10 categories (one category would be for example trading volumes for various products). Series from different categories are still highly correlated, but perhaps there is a specific approach best suited for dealing with data characterized by such knowledge? This presentation mentions something called 'constrained factor models' which could perhaps be more suitable than PCA Lasso or Relaimpo? I should mention that I'm also interested in the model being generally well interpretable.