How to fit a stepwise regression with ARIMA errors using Arima function in R?

Question

I am fitting a regression model with ARIMA errors in R using the Arima function from the forecast package. I assume that the function takes all predictors from a matrix that I assign to the xreg argument. Thus regression is fitted using all of them and the output is produced accordingly.

Now, I appreciate that coefficients with high p-values are likely to have no impact on the overall outcome, however I would like to understand how I could fit a stepwise regression using Arima function.

On a side note, how would I go about fitting a regularised regression (LASSO or ridge) with ARIMA errors -- either through Arima function, or other means?

Answer 1

Stepdown deleting non-significant arima structure married with stepup remedies base upon the "current set of model errors" possibly incorporating both arima structure and waiting to be discovered Intervention variables https://pdfs.semanticscholar.org/09c4/ba8dd3cc88289caf18d71e8985bdd11ad21c.pdf is quite useful as is described here Is it possible to automate time series forecasting? and here where @Adamo opines Interrupted Time Series Analysis - ARIMAX for High Frequency Biological Data?

Essentially arima model identification starts with the assumption of a simple mean nodel and then recursively adds structure that appears to be evidented/needed and proceeds until signal is separated from noise including stepping up when evidence is present regarding lack of constancy of the model error variance or lack of constancy of parameters over time . Modelling time series is much like peeling an onion to get to the heart of the matter i.e. the underlying sufficient signal.