A seasonality effect is a systematic pattern that repeats at regular temporal intervals in a time series. It is one source of nonstationarity, alongside long-term trend, because repeated fluctuations can make the series’ mean and variance change over time. section 7.0 section 7.3.5
Seasonality affects modeling in several practical ways:
- Remove seasonal patterns through seasonal differencing when a stationary series is required, recognizing that differencing reduces the available record count. section 7.3.6
- Model level, trend, and recurring fluctuations together with Holt–Winters exponential smoothing. section 7.4.7
- Choose additive seasonality for constant seasonal variation and multiplicative seasonality for changing seasonal variation. section 7.4.4
- Evaluate seasonal forecasts against alternatives using fit measures such as AIC and BIC, while checking forecast accuracy against observed values. section 7.4.7
Five-day seasonal cycle
A Holt–Winters model fitted with trend='add', seasonal='add', and seasonal_periods=5 assumes a recurring pattern every five trading days. Its forecast of Apple closing prices was slightly more accurate than the compared ARIMA forecast. section 7.4.7
>>> hw_model = ExponentialSmoothing(train, >>> trend = 'add', >>> seasonal = 'add', >>> seasonal_periods = 5).fit()
Inspect the compact Holt–Winters fitting example and its explicit additive trend, additive seasonality, and five-observation seasonal period. section 7.4.7
