seasonaltrend

Seasonal trend is a concept in time series analysis describing changes in the seasonal component of a series over time. Seasonality refers to regular, repeating patterns with a fixed period, such as monthly or quarterly fluctuations. A seasonal trend occurs when the magnitude, timing, or form of those seasonal patterns evolves as the overall level of the series changes, or when the seasonal cycle itself shifts over the analysis window.

In time series decomposition, data are often separated into trend, seasonal, and residual components. In additive models, the observed value is the sum of trend, seasonal, and residual parts; in multiplicative models, these parts multiply. A seasonal trend can arise when the seasonal amplitude grows or declines with the level of the series, or when seasonal timing shifts over time. Modern methods such as STL (seasonal-trend decomposition using LOESS) allow the seasonal pattern to vary in shape and strength, enabling a more flexible view of nonstationary seasonality.

Detection and modeling typically involve plotting, autocorrelation analysis, and formal decomposition. After isolating or removing the seasonal trend, analysts may forecast using models that handle evolving seasonality, such as SARIMA variants or TBATS, or apply seasonal adjustment techniques to obtain a clearer view of the underlying trend and irregular components.

Applications span economics, energy, retail, and climatology. Examples include increasing holiday-related demand in retail, growing summer electricity peaks in response to warming temperatures, and long-term shifts in seasonal temperature patterns due to climate change. Understanding seasonal trend improves forecasting accuracy and planning under changing seasonal dynamics.