Forecasting with multiple seasonal patterns using the Unobserved Components Model (UCM)

In the previous recipe, you were introduced to MSTL to decompose a time series with multiple seasonality. Similarly, the Unobserved Components Model (UCM) is a technique that decomposes a time series (with multiple seasonal patterns), but unlike MSTL, the UCM is also a forecasting model. Initially, the UCM was proposed as an alternative to the ARIMA model and introduced by Harvey in the book Forecasting, structural time series models and the Kalman filter, first published in 1989.

Unlike an ARIMA model, the UCM decomposes a time series process by estimating its components and does not make assumptions regarding stationarity or distribution. Recall, an ARIMA model uses differencing (the d order) to make a time series stationary.

There are situations where making a time series stationary – for example, through differencing – is not achievable. The time series can also contain...