# What is the difference between ARMA+Fourier and TBATS model?

I am just wondering that, in terms of the multi-seasonal time series forecast, what is the difference between

1. using auto.arima find the ARMA order, then fit arima and include xreg=fourier in.

2. using tbats

As ARMA+Fourier can also takes other covariates into account while tbats cannot, why people tend to use tbats one? Better performance in terms of forecasting?

## 1 Answer

I had the same question, and found this link here https://robjhyndman.com/hyndsight/dailydata/. In short, if you want to account for other regression coefficients (i.e. explicitly model a given holiday period), then you use Fourier and then ARIMA+regressor.

Note that if you want to fit a Fourier, then you will need to do some 10-fold cross-validation to get the best order of the Fourier. For example,

z <- fourier(ts(x, frequency=365.25), K=5) ## K is the parameter to be tuned.