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 (xt) as the sum of the trend cycle (Ft) and seasonal (St) components as follows:
xt = Ft + St + Єt
The residuals Єt 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 as product of the trend, seasonal, and irregular components is useful when there is time-varying seasonality:
xt = Ft x St x Єt
By taking logarithm, the multiplicative model is converted to an additive model of logarithm of the individual components. The multiplicative...
