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.
forecast
package for R. He said it would be difficult with the full ARIMA, because you'd have to wrap the lasso around the nonlinear ARIMA optimizer. One partial solution would be to fit an AR model usingglmnet
with lagged variables. As far as I know, no one's done this with a full ARIMA model yet. $\endgroup$