Dealing up with collinearity predictors' choice in xreg using auto.arima I'm trying to do a regression with arima errors in R, with xreg in auto.arima following https://otexts.com/fpp2/ by https://robjhyndman.com/ but I have some questions about the predictors' choice in xreg in auto.arima.
1) What should be done if the predictors x1,x2,x3 are higly correlated in xreg=cbind(x1,x2,x3)?
Is there a problem if the columns of matrix are highly correlated like in linear regression?
2) If 1) is yes, is there any automatic procedure to select no-multicollinearity predictors in auto.arima? Or auto.arima already do this when you launch it? Or i have to study multicollinearity of columns of matrix previously?
3) For forecasting, i have read that it doesn't matter if the predictors in auto.arima() are not significant. Is it right?
Thank you for the help.
 A: 1) Multicollinearity can be an issue and Hyndman discusses it in the text you link. It depends on the purpose of your forecast - for explanatory purposes, multicollinearity can be an issue, but if your purpose is the most accurate forecast, unless there's perfect multicollinearity is should not be an issue. You can check for multicollinearity by looking at the variance inflation factor. Secondly, multicollinearity just means that your p-values will be inaccurate. Even in linear regression, you can still make accurate predictions even if there's significant multicollinearity.
2) No, there is no automatic procedure to select non-multicollinear columns. In addition, passing the xreg argument to auto.arima does not select variables for your matrix in the AIC, you'd have to do that manually. It just does stepwise selection for the ARIMA model.
3) Yes, you are correct. Significance is often misunderstood to mean important - variables that are not significant may nonetheless still play an important part in prediction or explanation. In fact, the presence of multicollinearity may make significant variables insignificant due to the model being unable to distinguish between their effect on the response.
See the following:
[https://robjhyndman.com/hyndsight/to-explain-or-predict/][1]
[https://otexts.com/fpp2/causality.html][1]
