Stationary ARMA Processes

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

Abstract

In this chapter we introduce an extremely important class of time series {X t , t = 0, ± 1, ± 2,...} defined in terms of linear difference equations with constant coefficients. The imposition of this additional structure defines a parametric family of stationary processes, the autoregressive moving average or ARMA processes. For any autocovariance function γ(·) such that lim h→∞ γ(h) = 0, and for any integer k > 0, it is possible to find an ARMA process with autocovariance function γx(·) such that γx(h) = γ(h), 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 leads also to a very simple theory of linear prediction which is discussed in detail in Chapter 5.

Keywords

Autocorrelation Function Common Zero Stationary Time Series White Noise Process Linear Difference Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Peter J. Brockwell
    • 1
  • Richard A. Davis
    • 1
  1. 1.Department of StatisticsColorado State UniversityFort CollinsUSA

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