Decomposition of Time Series - Decomposition Based On Rates of Change

Decomposition Based On Rates of Change

This is an important technique for all types of time series analysis, especially for seasonal adjustment. It seeks to construct, from an observed time series, a number of component series (that could be used to reconstruct the original by additions or multiplications) where each of these has a certain characteristic or type of behaviour. For example, monthly or quarterly economic time series are usually decomposed into:

• the Trend Component that reflects the long term progression of the series (secular variation)
• the Cyclical Component that describes repeated but non-periodic fluctuations, possibly caused by the economic cycle
• the Seasonal Component reflecting seasonality (seasonal variation)
• the Irregular Component (or "noise") that describes random, irregular influences. It represents the residuals of the time series after the other components have been removed.

An example of statistical software for this type of decomposition is the program BV4.1 that is based on the so-called Berlin procedure.

Kendall shows an example of a decomposition into smooth, seasonal and irregular factors for a set of data containing values of the monthly aircraft miles flown by UK airlines.