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On The Invertibility Of Periodic Moving‐Average Models

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  • Mohamed Bentarzi
  • Marc Hallin

Abstract

. A sufficient condition for the invertibility of univariate periodic moving‐average models has been given by Cipra and Ghysels and Hall. We show that this condition is not a necessary one, and provide a necessary and sufficient condition for the general m‐variate, d‐periodical moving‐average MA(q) case.

Suggested Citation

  • Mohamed Bentarzi & Marc Hallin, 1994. "On The Invertibility Of Periodic Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 263-268, May.
    • Handle: RePEc:bla:jtsera:v:15:y:1994:i:3:p:263-268
    DOI: 10.1111/j.1467-9892.1994.tb00191.x
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    Cited by:

    1. Abdelouahab Bibi & Christian Francq, 2003. "Consistent and asymptotically normal estimators for cyclically time-dependent linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 41-68, March.
    2. Bentarzi, Mohamed, 1998. "Model-Building Problem of Periodically Correlatedm-Variate Moving Average Processes," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 1-21, July.
    3. Amaal Elsayed Mubarak & Ehab Mohamed Almetwally, 2024. "Modelling and Forecasting of Covid-19 Using Periodical ARIMA Models," Annals of Data Science, Springer, vol. 11(4), pages 1483-1502, August.
    4. Abdelhakim Aknouche & Abdelouahab Bibi, 2009. "Quasi‐maximum likelihood estimation of periodic GARCH and periodic ARMA‐GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 19-46, January.
    5. Hurd, H. & Makagon, A. & Miamee, A. G., 0. "On AR(1) models with periodic and almost periodic coefficients," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 167-185, July.
    6. Aknouche, Abdelhakim & Bentarzi, Mohamed, 2008. "On the existence of higher-order moments of periodic GARCH models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3262-3268, December.
    7. Qin Shao & Robert Lund, 2004. "Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 359-372, May.

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