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Practical Time Series Analysis by Dr. PKS Prakash, Dr. Avishek Pal

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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 ...

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