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:
- 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.
- 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.