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First-order seasonal autoregressive processes with periodically varying parameters


  • Basawa, I. V.
  • Lund, Robert
  • Shao, Qin


A time series model combining a first-order periodic autoregressive structure and the Box-Jenkins multiplicative seasonal autoregressive model is introduced. Stationarity conditions (in the periodic sense) for this so-called SPAR(1,1) process are established and its autocovariances are derived. Least-squares estimates of the model parameters are obtained and their limit distribution is derived. An extension to higher-order SPARMA models is suggested.

Suggested Citation

  • Basawa, I. V. & Lund, Robert & Shao, Qin, 2004. "First-order seasonal autoregressive processes with periodically varying parameters," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 299-306, May.
  • Handle: RePEc:eee:stapro:v:67:y:2004:i:4:p:299-306

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    References listed on IDEAS

    1. Parzen, Emanuel & Pagano, Marcello, 1979. "An approach to modeling seasonally stationary time series," Journal of Econometrics, Elsevier, vol. 9(1-2), pages 137-153, January.
    2. George E. P. Box & Steven Hillmer & George C. Tiao, 1979. "Analysis and Modeling of Seasonal Time Series," NBER Chapters,in: Seasonal Analysis of Economic Time Series, pages 309-346 National Bureau of Economic Research, Inc.
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    Cited by:

    1. Eugen Ursu & Pierre Duchesne, 2009. "Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(2), pages 183-212.


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