Time Series Decomposition: Separating Trend and Seasonality
Time series data often combine several underlying components: a long-term trend, repeating seasonal patterns, and random residual noise. By decomposing a series into these pieces, you can better understand its behavior and build more accurate forecasts.
Additive vs. Multiplicative Models
In an additive model, the components simply add together:
\[y_t = T_t + S_t + R_t\]where $T_t$ is the trend, $S_t$ is the seasonal component, and $R_t$ represents the residuals. A multiplicative model instead multiplies these terms:
\[y_t = T_t \times S_t \times R_t\]Choose the form that best fits the scale of seasonal fluctuations in your data.
Extracting the Components
Python libraries like statsmodels or pandas offer built-in functions to perform decomposition. Once the trend and seasonality are isolated, you can analyze them separately or remove them before applying forecasting models such as ARIMA.
Understanding each component allows you to explain past observations and produce more transparent predictions for future values.
