Best way to estimate contributors to process mean drift?

[#1]

Suppose I have a response metric Y which is seeing a sudden uptick in mean, while variance is similar. Assume it is influenced by upstream process factors, P1, P2, P3, P4.  What is the best way to estimate which of the process factors P1-P4 contributed most to the mean uptick? I have run POV analysis before to estimate contributors to variance, but is there a way to quantify similar effect on the mean drift? 

[#2]

Hi @jmdz ,

Is the process a continuous time series? If not, predictor screening is a good starting point, as well as forming a Fit Model with the linear terms (P1, P2, P3, P4) and potentially including some interactions or curvature (i.e. P1*P2, P1*P1).

Thanks,

Ben