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Computation and Characterization of Autocorrelations and Partial Autocorrelations in Periodic ARMA Models


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  • ROBERT Lund
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    This paper studies correlation and partial autocorrelation properties of periodic autoregressive moving-average (PARMA) time series models. An efficient algorithm to compute PARMA autocovariances is first derived. An innovations based algorithm to compute partial autocorrelations for a general periodic series is then developed. Finally, periodic moving averages and autoregressions are characterized as periodically stationary series whose autocovariances and partial autocorrelations, respectively, are zero at all lags that exceed some periodically varying threshold. Copyright 2004 Blackwell Publishing Ltd.

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    Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

    Volume (Year): 25 (2004)
    Issue (Month): 3 (05)
    Pages: 359-372

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    Handle: RePEc:bla:jtsera:v:25:y:2004:3:p:359-372

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    Cited by:
    1. Shao, Q., 2006. "Mixture periodic autoregressive time series models," Statistics & Probability Letters, Elsevier, Elsevier, vol. 76(6), pages 609-618, March.
    2. Roy, Roch & Saidi, Abdessamad, 2008. "Aggregation and systematic sampling of periodic ARMA processes," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(9), pages 4287-4304, May.
    3. Shao, Q. & Ni, P.P., 2004. "Least-squares estimation and ANOVA for periodic autoregressive time series," Statistics & Probability Letters, Elsevier, Elsevier, vol. 69(3), pages 287-297, September.
    4. Francq, Christian & Roy, Roch & Saidi, Abdessamad, 2011. "Asymptotic properties of weighted least squares estimation in weak parma models," MPRA Paper 28721, University Library of Munich, Germany.
    5. Anderson, Paul L. & Kavalieris, Laimonis & Meerschaert, Mark M., 2008. "Innovations algorithm asymptotics for periodically stationary time series with heavy tails," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 99(1), pages 94-116, January.


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