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Model-Building Problem of Periodically Correlatedm-Variate Moving Average Processes

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  • Bentarzi, Mohamed
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    Abstract

    The model-building problem of periodically correlatedm-variateq-dependent processes is considered. We show that for a given periodical autocovariance function of anm-variateMA(q) process there are two particular corresponding classes (that may reduce to one class) of periodic (equivalent) models. Furthermore, any other (intermediate) model is not periodic. It is, however, asymptotically periodic. The matrix coefficients of the particular periodic models are given in terms of limits of some periodic matrix continued fractions, which are a generalization of the classical periodic continued fractions (Wall, 1948). These periodic matrix continued fractions are particular solutions of some prospective and/or retrospective recursion equations, arising from the symbolic factorization of the associated linear autocovariance operator. In addition, we establish a procedure to calculate these limits. Numerical examples are given for the simple cases of periodically correlated univariate one- and two-dependent processes.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 66 (1998)
    Issue (Month): 1 (July)
    Pages: 1-21

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    Handle: RePEc:eee:jmvana:v:66:y:1998:i:1:p:1-21

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    Related research

    Keywords: periodically correlated moving average process; model-building problem; symbolic factorization; autocovariance operator; periodic matrix continued fraction;

    References

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    1. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
    2. Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June.
    3. Bentarzi, Mohamed & Hallin, Marc, 1996. "Locally Optimal Tests against Periodic Autoregression: Parametric and Nonparametric Approaches," Econometric Theory, Cambridge University Press, vol. 12(01), pages 88-112, March.
    4. Marc Hallin & Mohamed Bentarzi, 1994. "On the invertibility of periodic moving-average models," ULB Institutional Repository 2013/2047, ULB -- Universite Libre de Bruxelles.
    5. 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.
    6. 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.
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    Cited by:
    1. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "On some probabilistic properties of double periodic AR models," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 407-413, February.

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