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 j : i = 1,..., p; j= 1,..., q} and the white noise variance σ2, 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 AIC statistic discussed in Chapter 9.

Keywords

Maximum Likelihood Estimator ARMA Model ARMA Process Sample Autocorrelation Innovation Algorithm 
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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