World Library  
Flag as Inappropriate
Email this Article

Decomposition of time series

Article Id: WHEBN0007579995
Reproduction Date:

Title: Decomposition of time series  
Author: World Heritage Encyclopedia
Language: English
Subject: Time series, Statistics, List of statistics articles, Singular spectrum analysis, Time series analysis
Collection: Time Series Analysis
Publisher: World Heritage Encyclopedia

Decomposition of time series

The decomposition of time series is a statistical method that deconstructs a time series into notional components. There are two principal types of decomposition which are outlined below.


  • Decomposition based on rates of change 1
  • Decomposition based on predictability 2
  • Examples 3
  • Software 4
  • See also 5
  • References 6
  • Further reading 7

Decomposition based on rates of change

This is an important technique for all types of time series analysis, especially for seasonal adjustment.[1] 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 T_t that reflects the long term progression of the series (secular variation)
  • the Cyclical Component C_t that describes repeated but non-periodic fluctuations
  • the Seasonal Component S_t reflecting seasonality (seasonal variation)
  • the Irregular Component I_t (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).[1] See Wold's theorem and Wold decomposition.


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.[2]


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

See also


  1. ^ a b Dodge, Y. (2003). The Oxford Dictionary of Statistical Terms. New York: Oxford University Press.  
  2. ^ Kendall, M. G. (1976). Time-Series (Second ed.). Charles Griffin. (Fig. 5.1).  

Further reading

  • Enders, Walter (2004). "Models with Trend". Applied Econometric Time Series (Second ed.). New York: Wiley. pp. 156–238.  
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.