Parameter estimation of an autoregressive moving average model

  • Junji Nakano
Article
  • 62 Downloads

Summary

An estimator of the set of parameters of an autoregressive moving average model is obtained by applying the method of least squares to the log smoothed periodogram. It is shown to be asymptotically efficient and normally distributed under the normality and the circular condition of the generating process. A computational procedure is constructed by the Newton-Raphson method. Several computer simulation results are given to demonstrate the usefulness of the present procedure.

Keywords

Maximum Likelihood Estimator Average Model Circular Condition Prediction Error Variance Scalar Time Series 

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References

  1. [1]
    Anderson, T. W. (1977). Estimation for autoregressive moving average models in the time and frequency domains,Ann. Statist.,5, 842–865.MATHMathSciNetGoogle Scholar
  2. [2]
    Bloomfield, P. (1973). An exponential model for the spectrum of a scalar time series,Biometrika,60, 217–226.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Cleveland, W. S. (1972_. The inverse autocorrelations of a time series and their applications,Technometrics,14, 277–298.MATHCrossRefGoogle Scholar
  4. [4]
    Clevenson, M. L. (1970). Asymptotically efficient estimates of the parameters of a moving average time series, Ph.D. Dissertation, Department of Statistics, Stanford University.Google Scholar
  5. [5]
    Davis, H. T. and Jones, R. H. (1968). Estimation of the innovation variance of a stationary time series,J. Amer. Statist. Ass.,63, 141–149.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Durbin, J. (1960). The fitting of time-series models,Rev. Inst. Internat. Statist.,28, 233–244.MATHCrossRefGoogle Scholar
  7. [7]
    Hannan, E. J. (1969). The estimation of mixed moving average autoregressive systems,Biometrika,56, 579–593.MATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    Hannan, E. J. and Nicholls, D. F. (1977). The estimation of the prediction error variance,J. Amer. Statist. Ass.,72, 834–840.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    McClave, J. T. (1974). A comparison of moving average estimation procedures,Commun. Statist.,3, 865–883.MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Singleton, R. C. (1969). An algorithm for computing the mixed radix fast Fourier transform,IEEE Trans. Audio and Electro., AU-17, 93–103.CrossRefGoogle Scholar
  11. [11]
    Wahba, G. (1980). Automatic smoothing of the log periodogram,J. Amer. Statist. Ass.,75, 122–132.MATHCrossRefGoogle Scholar
  12. [12]
    Walker, A. M. (1962). Large-sample estimation of parametes for autoregressive processes with moving-average residuals,Biometrika,49, 117–131.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1982

Authors and Affiliations

  • Junji Nakano
    • 1
  1. 1.Technical College of the University of TokushimaTokushimaJapan

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