Time series regression

noetsi

Fortran must die
#1
What is the best and simplest form of time series regression. I have looked at lots and there are major issues with complexity and how to deal with variables when one is stationary and the other is not.

I want to know how two or more predictors are influencing Y over time. I am not concerned here with autocorrelation...I know how to deal with that. But simply predicting correctly the change in Y over time if X changes over time.

This is something I have tried to repeatedly learn how to do for a decade without success. I am using vector autoregressive models but I have a lot of trouble interpreting them.
 

noetsi

Fortran must die
#2
On a different level, is it true that squaring time, quadratic approaches to regression, are frowned on now. That used to be a common suggestion to deal with non-linear models.