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Asymptotic Results For Periodic Autoregressive Moving‐Average Processes

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  • P. L. Anderson
  • A. V. Vecchia

Abstract

. This paper is concerned with the derivation of asymptotic distributions for the sample autocovariance and sample autocorrelation functions of periodic autoregressive moving‐average processes, which are useful in modelling periodically stationary time series. In an effort to obtain a parsimonious model representing a periodically stationary time series, the asymptotic properties of the discrete Fourier transform of the estimated periodic autocovariance and autocorrelation functions are presented. Application of the asymptotic results to some specific models indicates their usefulness for model identification analysis.

Suggested Citation

  • P. L. Anderson & A. V. Vecchia, 1993. "Asymptotic Results For Periodic Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(1), pages 1-18, January.
    • Handle: RePEc:bla:jtsera:v:14:y:1993:i:1:p:1-18
    DOI: 10.1111/j.1467-9892.1993.tb00126.x
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    Cited by:

    1. Paul L. Anderson & Mark M. Meerschaert, 2005. "Parameter Estimation for Periodically Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 489-518, July.
    2. G. J. Adams & G. C. Goodwin, 1995. "Parameter Estimation For Periodic Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 127-145, March.
    3. Paul L. Anderson & Farzad Sabzikar & Mark M. Meerschaert, 2021. "Parsimonious time series modeling for high frequency climate data," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 442-470, July.

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