Time series may exhibit multiple seasonalities, e.g., retail sales have intra-weekly and yearly seasonality, and electricity load (and price) has intra-daily, intra-weekly and yearly seasonality.
One standard way of modeling and forecasting time series with multiple seasonalities is the TBATS model (De Livera, Hyndman & Snyder, 2011, JASA). It is implemented in the
tbats() function in the
forecast package for R. See the related tbats tag. More info can be found in section 11.1 of Forecasting: Principles and Practice (2nd ed.) by Athanasopoulos & Hyndman.
Alternatively, Bandara et al. (2021) propose an algorithm to decompose a time series into multiple additive seasonal components, analogously to the standard STL decomposition. The components can then be forecasted separately and added together. The MSTL algorithm is also implemented in the
forecast package for R.