Seasonal decomposition techniques in time series analysis are methods used to break down a time series into its fundamental components: trend, seasonality, and residuals (or noise). The goal of these techniques is to isolate and better understand the underlying patterns in the data. Trend refers to the long-term movement in the series, seasonality captures the repeating patterns at fixed intervals (like monthly sales spikes), and residuals are the random variations that are not explained by the trend or seasonal factors.
One commonly used method for seasonal decomposition is the Seasonal-Trend decomposition using LOESS (STL). STL allows for flexible modeling of both trend and seasonality by applying locally weighted regression to smooth the data. This method is particularly useful because it can handle seasonal variations that change over time. For example, if a retail store experiences varying peaks during holiday seasons, STL can adapt to those shifts, making it easier to forecast future sales more accurately.
Another method is the classical additive or multiplicative decomposition. In the additive model, the time series is expressed as the sum of its components: Y(t) = Trend(t) + Seasonality(t) + Residual(t). Conversely, the multiplicative model expresses it as Y(t) = Trend(t) × Seasonality(t) × Residual(t). The choice between additive and multiplicative decomposition usually depends on the nature of the data. For instance, if the amplitude of seasonal fluctuations increases as the trend increases (like higher sales during holiday seasons with overall growth), a multiplicative model might be more appropriate. Overall, these techniques help developers create better predictive models and make informed business decisions based on data-driven insights.