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I have a non-stationary output time-series (oil prices) that is to be forecasted with 20 different input time series. The series are all non-stationary. I am considering two approaches.

Approach 1) Using R's auto.arima
Here I am stuck on how to adjust for non-stationarity as well as how to consider lags and leads of the covariates. Do I consider differenced versions of the regressors in the xreg argument? I also want to consider lags and leads. Should I transform the predictors to the lags and lead values and then input them to auto.arima using xreg? What about the output oil price series - should I difference it too before using it ? However, I need to forecast the non-differenced series.

Approach 2)
I read this on R's help somewhere. Step 1: build a linear model,step 2: run auto.arima on the residuals and finally step 3: build an ARIMA model on the original series with the order (p,d,q) as determined in step 2. My question again is do I difference the series to make them stationary before building the linear model, as well as use lag and lead transformations on the predictors. Again, my interest is in forecasting the untransformed oil price series.

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With respect to your question the model should incorporate any need transformations if the covariates including powertransformations , differencing , lead and lag structure and of course any identified Pulses, level,step shifts, local time trends that have been empirically identified.

When you have built a model and are using predicted values for the user-specified covariates make sure you are taking into account their uncertainty when you are computing the prediction confidence limits for your output series. This important issue was raised and answered in ARIMAX - predict .

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  • $\begingroup$ Should I explicitly model the leads and lags even if I'm using auto.arima ? I wasn't sure if auto.arima takes care of differencing the covariates on its own. That's really my question. $\endgroup$ – user2450223 Jan 21 at 14:13
  • $\begingroup$ i don't believe auto.arima has the required functionality to empirically identify the nature of the leads and lags OR transformations for the covariates. That appears to be on you $\endgroup$ – IrishStat Jan 21 at 14:59

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