Time series and forecasting · insight-0223

Model each seasonal period explicitly in hourly or daily data

Situation
Hourly electricity load shows daily, weekly and annual cycles, and a model with one seasonal period leaves strong patterns in the residuals.
Action
Use methods that accept several seasonal periods, such as STL with multiple periods or Fourier terms per period in a regression with ARIMA errors, or calendar features in an ML model, and inspect residual ACF at each period's lags.
Reason
Daily and sub-daily data often contain multiple seasonal patterns that need separate components.
Boundary
Energy, call centres, web traffic, airport passenger flows, retail footfall.

Symptom or risk

A single seasonal period forces the other cycles into the trend or noise, which inflates errors and makes intervals too wide or biased.

Short histories may not contain enough annual cycles to estimate annual seasonality; use fewer Fourier terms or external calendars.

Many Fourier terms overfit; choose their number by information criterion or backtest.

Using a seasonal period of 8760 hours in a model that needs integer seasonal lags and huge state.

For complex seasonality, FPP3 proposes STL with multiple seasonal periods and dynamic harmonic regression with Fourier terms for each period.
Forecasting: Principles and Practice (3rd edition)