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First-order seasonal autoregressive processes with periodically varying parameters

Author

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

Abstract

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

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    1. Robert Lund & I. V. Basawa, 2000. "Recursive Prediction and Likelihood Evaluation for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 75-93, January.
    2. 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.
    3. I. V. Basawa & Robert Lund, 2001. "Large Sample Properties of Parameter Estimates for Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 651-663, November.
    4. 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.
    5. Peter Bloomfield & Harry L. Hurd & Robert B. Lund, 1994. "Periodic Correlation In Stratospheric Ozone Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 127-150, March.
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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, May.
    2. 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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