# Training and sampling for static model in multivariate time series

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:

1. 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 ?

2. Should I consider randomly shuffling the training set before the training ? Or anyway, is there some issues related to it I could face ?

3. What's the best accuracy to use ? R2 or Mean Relative Error ?

Thanks