TBATS is a time series model that is useful for handling data with multiple seasonal patterns. TBATS is an acronym for key features of the model: T: Trigonometric seasonality B: Box-Cox transformation A: ARIMA errors T: Trend S: Seasonal components.
The first step towards fitting a TBATS model is to apply a Box-Cox transformation to the data. This is a flexible way to select and apply a power transformation to a series to obtain a shape which is easy to model. A parameter λλ between −5 and 5 is selected such that the transformation
will yield data that follows a normal distribution curve as closely as possible.
The model is then fitted using a combination of ARMA (see Advanced: ARIMA), exponential smoothing (see Advanced: ETS) and multiple seasonal patterns. Which of the components to include is selected based on Akaike's Information Criterion (AIC) which favors a simpler model over a more complicated while also prioritizing what fits the data best.