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Estimation for ARMA Models

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

Abstract

The determination of an appropriate ARMA(p, q) model to represent an observed stationary time series involves a number of inter-related problems. These include the choice of p and q (order selection), and estimation of the remaining parameters, i.e. the mean, the coefficients {φ i , θ j : i = 1,..., p; j = 1,..., q} and the white noise variance σ 2, for given values of p and q. Goodness of fit of the model must also be checked and the estimation procedure repeated with different values of p and q. Final selection of the most appropriate model depends on a variety of goodness of fit tests, although it can be systematized to a large degree by use of criteria such as the AICC statistic discussed in Chapter 9.

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

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

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