Decomposition of time series
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, time series are usually decomposed into:
- the Trend Component <math>T_t</math> that reflects the long term progression of the series (secular variation)
- the Cyclical Component <math>C_t</math> that describes repeated but non-periodic fluctuations
- the Seasonal Component <math>S_t</math> reflecting seasonality (seasonal variation)
- the Irregular Component <math>I_t</math> (or "noise") that describes random, irregular influences. It represents the residuals of the time series after the other components have been removed.
Decomposition based on predictability
The theory of time series analysis makes use of the idea of decomposing a times series into deterministic and non-deterministic components (or predictable and unpredictable components). See Wold's theorem and Wold decomposition.
- Enders, Walter (2004). "Models with Trend". Applied Econometric Time Series (Second ed.). New York: Wiley. pp. 156–238. ISBN 0-471-23065-0.