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rtime-serieslinear-regressionforecastingarima
Sanna Vilkki
Sanna Vilkki

Reputation: 11

Does auto.arima function in R do the differencing for the y- and x-variables before or after estimating the linear regression model?

I'm trying to estimate a linear regression with arima errors, but my regressors are highly collinear and thus the regression model suffers from multicollinearity. Since my ultimate goal is to be able to interpret the individual regression coefficients as elasticities and to use them for ex-ante forecasting, I need to solve the multicollinearity somehow to be able to trust the coefficients of the regressors. I know that transforming the regressor variables eg. by differencing might help to reduce the multicollinearity. And I have also understood that auto.arima performs the same differencing for both the response variable as well as the regressors defined in xreg (see: Do we need to do differencing of exogenous variables before passing to xreg argument of Arima() in R?).

So my question is, does it do the transformation already before estimating the regression coefficients or is the regression estimated using the untransformed data and transformation done only before fitting the arima model to the errors? And if the transformation is done before estimating the regression, what is the script to get those transformed values to a table or something, to be able to run the multicollinearity test on those rather than the original data?

Upvotes: 1

Views: 1508

Answers (1)

Rob Hyndman
Rob Hyndman

Reputation: 31800

The auto.arima() function will do the differencing before estimation to ensure consistent estimators. The estimation of the regression coefficients and ARIMA model is done simultaneously using MLE.

You can manually difference the data yourself using the diff() function.

Upvotes: 2

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