I use the auto.arima() function in the forecast package to fit ARMAX models with a variety of covariates. However, I often have a large number of variables to select from and usually end up with a final model that works with a subset of them. I don't like ad-hoc techniques for variable selection because I am human and subject to bias, but cross-validating time series is hard, so I haven't found a good way to automatically try different subsets of my available variables, and am stuck tuning my models using my own best judgement.
When I fit glm models, I can use the elastic net or the lasso for regularization and variable selection, via the glmnet package. Is there a existing toolkit in R for using the elastic net on ARMAX models, or am I going to have to roll my own? Is this even a good idea?
edit: Would it make sense to manually calculate the AR and MA terms (say up to AR5 and MA5) and the use glmnet to fit the model?
edit 2: It seems that the FitAR package gets me part, but not all, of the way there.