Let's suppose I have two time series $x_t$ and $y_t$. I also assume there is an underlying static model of the form:
$$ y_t=f(x_t) + \epsilon_t $$
As I said I consider the model a static model meaning there is no influence of past value of both of time series but the effect is immediate. As such, I would like to use my favorite ML algorithm to infer the unknown function $f$. Now the questions/confusions are:
In order to construct my training set, should I use some sampling method to extract i.i.d. points to be used in a purely regression context ?
Should I consider randomly shuffling the training set before the training ? Or anyway, is there some issues related to it I could face ?
What's the best accuracy to use ? R2 or Mean Relative Error ?