seasonalities

Seasonality refers to regular, predictable fluctuations in a time series that recur at or near fixed periods within a year or other calendar cycles. In practice, the term seasonality is used to describe the phenomenon, while seasonalities can refer to multiple, domain-specific seasonal patterns. Seasonal effects are superimposed on longer-term trends and can occur at annual, quarterly, monthly, weekly, or daily intervals. Seasonality implies that observations from the same season across different years tend to be more similar to each other than observations from different seasons.

Causes include astronomical and climatic cycles (seasonal temperature and daylight), cultural and economic calendars (holidays, school terms, fiscal quarters), and behavioral patterns (weather-driven demand). Seasonality can be additive, where fluctuations are independent of level, or multiplicative, where fluctuations scale with the series level. Common examples include higher retail sales during holidays, increased energy demand in winter, and biological cycles in plants and animals.

Analysis and use: Seasonality is often estimated and removed using decomposition methods such as additive or multiplicative classical decomposition, STL, or model-based approaches like X-13ARIMA-SEATS. Seasonally adjusted data remove predictable seasonal components to reveal the underlying trend. Strength and periodicity can be assessed with seasonal indices, autocorrelation at seasonal lags, and spectral analysis. Forecasting models may incorporate seasonality via seasonal ARIMA, Fourier terms, or seasonal components.

Applications and considerations: Accounting for seasonality improves forecasting, budgeting, and planning in retail, manufacturing, energy, agriculture, and public health. Seasonality can evolve over time due to climate change, policy shifts, or market structure, requiring periodic revision of seasonal factors. Nonstationary seasonality or changing calendar effects poses challenges for modeling and interpretation.