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Innovations algorithm asymptotics for periodically stationary time series with heavy tails

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  • Anderson, Paul L.
  • Kavalieris, Laimonis
  • Meerschaert, Mark M.
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    Abstract

    The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper we compute the asymptotic distribution for these estimates in the case where the underlying noise sequence has infinite fourth moment but finite second moment. In this case, the sample covariances on which the innovations algorithm are based are known to be asymptotically stable. The asymptotic results developed here are useful to determine which model parameters are significant. In the process, we also compute the asymptotic distributions of least squares estimates of parameters in an autoregressive model.

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    Bibliographic Info

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

    Volume (Year): 99 (2008)
    Issue (Month): 1 (January)
    Pages: 94-116

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    Handle: RePEc:eee:jmvana:v:99:y:2008:i:1:p:94-116

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    Keywords: Time series Periodically stationary Innovations algorithm;

    References

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    1. Brockwell, P. J. & Davis, R. A., 1988. "Simple consistent estimation of the coefficients of a linear filter," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 47-59, April.
    2. Anderson, Paul L. & Meerschaert, Mark M. & Vecchia, Aldo V., 1999. "Innovations algorithm for periodically stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 149-169, September.
    3. 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, 05.
    4. Paul L. Anderson & Mark M. Meerschaert, 2005. "Parameter Estimation for Periodically Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 489-518, 07.
    5. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
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