I am working on economic data, explaining industries behaviours regarding economic cycle. For each industry I have around 30 independent factors. My Y explained variable is weekly stocks returns. Factors characteristics are:

• Some are correlated with the Y, and good at explaining the short term noise of my Y. Thus, they are performing decently in linear models.
• Some have good significance in specific periods, thus they are significant for some months or year when I make a dynamic estimation through Kalman filtering estimation for example.
• Last, some seem relevant in-sample when working by pair-conditioning or even triple-conditioning. (Y is strongly significantly negative for example when both x1 is positive and x2 is negative, but not significant in any other cases).

I struggle at modeling in a robust way the last type (multi-case-specific-variables). I considered using SVM, Neural-Network or tree-algorithm, but I'm not sure which would be the best for now.

My question is: What Algorithm would you recommend to explain the 3rd type of phenomena? What Algorithm (if any) would you recommend to explain the 3 of them?