# Sensitivity analysis in time series forecasting

Given a data set consisting of features time signals $$X=[x_1,\dots, x_n]$$ and one target time series $$y$$, I would like to study the sensitivity of $$y$$ with each of the $$x$$'s.

What I think:

1. Compute finite differences given the data. But I am not sure about this approach as finite differences assume smooth functions and might lead to very large errors. Also it is a very simplistic approach that doesn't take into account the real physics in the problem.
2. Train a neural network (i.e, LSTM / GRU) for $$y$$ prediction, then make use of automatic differentiation to calculate the derivative of the network (that is $$y$$) wrt the inputs $$X$$. But that would be a post-modeling approach.

I didn't find a lot on that topic in the literature and I would really appreciate any hints and help.