Estimation of the Mean and the Autocovariance Function

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

Abstract

If {X t } is a real-valued stationary process, then from a second-order point of view it is characterized by its mean μ and its autocovariance function γ(·). The estimation of μ, γ(·) and the autocorrelation function ρ(·) = γ(·)/γ(0) from observations of X 1,..., X n , therefore plays a crucial role in problems of inference and in particular in the problem of constructing an appropriate model for the data. In this chapter we consider several estimators which will be used and examine some of their properties.

Keywords

Asymptotic Distribution White Noise Process Autocovariance Function Good Linear Unbiased Estimator Sample Autocorrelation 
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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