Difference Predictors in Auto.Arima Forecast

Question

I'm trying to build an auto.arima forecast with predictors like the example below. I've noticed that my predictor is non-stationary. So I was wondering if I should difference the predictor before inputting it in the xreg parameter, like I've shown below. The real data set is much larger, this just an example. Any advice is greatly appreciated.

Code:

tsTrain <-tsTiTo[1:60]
tsTest <- tsTiTo[61:100]

ndiffs(ds$CustCount)
##returns 1

diffedCustCount<-diff(ds$CustCount,differences=1)

Xreg<-diffedCustCount[1:100]

##Predictor
xregTrain2 <- Xreg[1:60]
xregTest2 <- Xreg[61:100]


Arima.fit2 <- auto.arima(tsTrain, xreg = xregTrain2)

Acast2<-forecast(Arima.fit2, h=40, xreg = xregTest2)

Data:

dput(ds$CustCount[1:100])

c(3, 3, 1, 4, 1, 3, 2, 3, 2, 4, 1, 1, 5, 6, 8, 5, 2, 7, 7, 3, 2, 2, 2, 1, 3, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 2, 3, 7, 5, 6, 8, 7, 3, 5, 6, 6, 8, 4, 2, 1, 2, 1, NA, NA, 4, 2, 2, 4, 11, 2, 8, 1, 4, 7, 11, 5, 3, 10, 7, 1, 1, NA, 2, NA, NA, 2, NA, NA, 1, 2, 3, 5, 9, 5, 9, 6, 6, 1, 5, 3, 7, 5, 8, 3, 2, 6, 3, 2, 3, 1 )

dput(tsTiTo[1:100])

c(45, 34, 11, 79, 102, 45, 21, 45, 104, 20, 2, 207, 45, 2, 3, 153, 8, 2, 173, 11, 207, 79, 45, 153, 192, 173, 130, 4, 173, 174, 173, 130, 79, 154, 4, 104, 192, 153, 192, 104, 28, 173, 52, 45, 11, 29, 22, 81, 7, 79, 193, 104, 1, 1, 46, 130, 45, 154, 153, 7, 174, 21, 193, 45, 79, 173, 45, 153, 45, 173, 2, 1, 2, 1, 1, 8, 1, 1, 79, 45, 79, 173, 45, 2, 173, 130, 104, 19, 4, 34, 2, 192, 42, 41, 31, 39, 11, 79, 4, 79)

Answer 1

The xreg argument in auto.arima performs a dynamic regression which is to say that you are performing a linear regression and fitting the errors with an arma process.

While auto.arima() used to require manual differencing for non-stationary data when external regressors are included, this is no longer the case. auto.arima() will take non-stationary data as an input and determine the order of differencing using a unit-root test.

See this Post from Rob Hyndman for further detail.