Suitable Machine Learning algorithm for multi-conditionned variables?

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?

Are you trying to discover the feature pairs and triples? I'd attack that third one with random forest; the associations should show up as closely linked in the "successful" trees. You could also try a feature reduction; a variable closely linked to one or two others will be dominated and removed.

Also, have you considered a FFT (fast Fourier transform) to analyze cyclic noise in the observations?

I cannot recommend any one algorithm to explain all three phenomena. First of all, you haven't given us anything to describe the shape and texture of the data. Second, the available analysis models are almost certainly too simplistic and general to perform such a deep analysis in one pass.