TBATS with regressors

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I’ve received a few emails about including regression variables (i.e., covariates) in TBATS models. As TBATS models are related to ETS models, tbats() is unlikely to ever include covariates as explained here. It won’t actually complain if you include an xreg argument, but it will ignore it.

When I want to include covariates in a time series model, I tend to use auto.arima() with covariates included via the xreg argument. If the time series has multiple seasonal periods, I use Fourier terms as additional covariates. See my post on forecasting daily data for some discussion of this model. Note that fourier() and fourierf() now handle msts objects, so it is very simple to do this.

For example, if holiday contains some dummy variables associated with public holidays and holidayf contains the corresponding variables for the first 100 forecast periods, then the following code can be used:

y <- msts(x, frequency=c(7,365.25))
z <- fourier(y, K=c(5,5))
zf <- fourierf(y, K=c(5,5), h=100)
fit <- auto.arima(y, xreg=cbind(z,holiday), seasonal=FALSE)
fc <- forecast(fit, xreg=cbind(zf,holidayf), h=100)

The main disadvantage of the ARIMA approach is that the seasonality is forced to be periodic, whereas a TBATS model allows for dynamic seasonality.

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