Stepwise selection of exogenous features

[dilwong]

A potentially useful feature could be for pmdarima.arima.auto_arima to stepwise determine (using the selected information_criterion) which exogenous features should be included in the model (e.g. add/remove columns in X to optimize the AIC).

[tgsmith61591]

This is a cool idea. I think practically the best way to handle this would be to create an exog transformer that performs feature selection (i.e., similar to sklearn VarianceThreshold) that could be included in a Pipeline object. Then, I bet we could bootstrap the sklearn RandomSearchCV or GridSearchCV classes to do this.

If you'd like to take a swing at this, please feel free. Otherwise it may be some time before we get around to this enhancement.