Stationary Processes

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


A key role in time series analysis is played by processes whose properties, or some of them, do not vary with time. If we wish to make predictions, then clearly we must assume that something does not vary with time. In extrapolating deterministic functions it is common practice to assume that either the function itself or one of its derivatives is constant. The assumption of a constant first derivative leads to linear extrapolation as a means of prediction. In time series analysis our goal is to predict a series that typically is not deterministic but contains a random component. If this random component is stationary, in the sense of Definition 1.4.2, then we can develop powerful techniques to forecast its future values. These techniques will be developed and discussed in this and subsequent chapters.


Autocorrelation Function Stationary Time Series Autocovariance Function ARMA Process White Noise Sequence 


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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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