ARMA Models

  • Peter J. Brockwell
  • Richard A. Davis
Part of the Springer Texts in Statistics book series (STS)


In this chapter, we introduce an important parametric family of stationary time series, the autoregressive moving average or ARMA processes. For a large class of autocovariance functions γ (•), it is possible to find an ARMA process {X t } with ACVF γ X (·) such that γ(·) is well approximated by γ X (·). In particular, for any positive integer K, there exists an ARMA process {X t } such that γ X (h) = γ(h) for h = 0, 1,.... K. For this (and other) reasons, the family of ARMA processes plays a key role in the modelling of time series data. The linear structure of ARMA processes also leads to a substantial simplification of the general methods for linear prediction discussed earlier in Section 2.5.


Sunspot Number ARMA Model Stationary Time Series Autocovariance Function ARMA Process 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Peter J. Brockwell
    • 1
  • Richard A. Davis
    • 2
  1. 1.Royal Melbourne Institute of TechnologyMelbourneAustralia
  2. 2.Department of StatisticsColorado State UniversityFort CollinsUSA

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