# Regularize Regression with ARIMA errors in R

I am fitting regression with ARIMA errors in R. The xreg variables could be correlated with each other. Plus, I may be over-fitting my models. So, to handle both multicolinearity and over-fitting problems, I want to regularize my models. Is it possible to use linear models such as lasso, ridge and elastic net in regression with ARIMA errors?

• You could implement it, but it's probably going to be slow and not very good. I'm not convinced from the problem description that you need penalized likelihood. Penalized likelihood, after all, gives you biased estimates. It is a direct solution to $p \gg n$, but that's not your problem. The L1 penalty prefers covariates that are "big" which is going to exacerbate any collinearity issues due to their variance inflation. – AdamO Sep 5 '19 at 21:40
• Check out stats.stackexchange.com/questions/152202. – Richard Hardy Sep 6 '19 at 8:28