Practical Time Series Analysis

Time series decomposition

The objective of time series decomposition is to model the long-term trend and seasonality and estimate the overall time series as a combination of them. Two popular models for time series decomposition are:

• Additive model
• Multiplicative model

The additive model formulates the original time series (x_t) as the sum of the trend cycle (F_t) and seasonal (S_t) components as follows:

x_t = F_t + S_t + Є_t

The residuals Є_t obtained after adjusting the trend and seasonal components are the irregular variations. The additive model is usually applied when there is a time-dependent trend cycle component, but independent seasonality that does not change over time.

The multiplicative decomposition model, which gives the time series ...