IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v99y2008i1p94-116.html
   My bibliography  Save this article

Innovations algorithm asymptotics for periodically stationary time series with heavy tails

Author

Listed:
  • Anderson, Paul L.
  • Kavalieris, Laimonis
  • Meerschaert, Mark M.

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.

Suggested Citation

  • 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, vol. 99(1), pages 94-116, January.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:1:p:94-116
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(07)00029-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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, July.
    3. 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.
    4. 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.
    5. Dag Tjøstheim & Jostein Paulsen, 1982. "Empirical Identification Of Multiple Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 265-282, July.
    6. 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.
    7. 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.
    8. G. J. Adams & G. C. Goodwin, 1995. "Parameter Estimation For Periodic Arma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 127-145, March.
    9. 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.
    10. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Aleksandra Grzesiek & Prashant Giri & S. Sundar & Agnieszka WyŁomańska, 2020. "Measures of Cross‐Dependence for Bidimensional Periodic AR(1) Model with α‐Stable Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 785-807, November.
    3. Yorghos Tripodis & Jeremy Penzer, 2009. "Modelling time series with season-dependent autocorrelation structure," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(7), pages 559-574.
    4. Roy, Roch & Saidi, Abdessamad, 2008. "Aggregation and systematic sampling of periodic ARMA processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4287-4304, May.
    5. Christian Francq & Roch Roy & Abdessamad Saidi, 2011. "Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 699-723, November.
    6. Shao, Q. & Ni, P.P., 2004. "Least-squares estimation and ANOVA for periodic autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 287-297, September.
    7. Jiajie Kong & Robert Lund, 2023. "Seasonal count time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 93-124, January.
    8. Shao, Q., 2006. "Mixture periodic autoregressive time series models," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 609-618, March.
    9. 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, July.
    10. 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.
    11. 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.
    12. 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.
    13. Amaral, Luiz Felipe & Souza, Reinaldo Castro & Stevenson, Maxwell, 2008. "A smooth transition periodic autoregressive (STPAR) model for short-term load forecasting," International Journal of Forecasting, Elsevier, vol. 24(4), pages 603-615.
    14. L. Tang & Q. Shao, 2014. "Efficient Estimation For Periodic Autoregressive Coefficients Via Residuals," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 378-389, July.
    15. ŁUkasz Lenart & Jacek Leśkow & Rafał Synowiecki, 2008. "Subsampling in testing autocovariance for periodically correlated time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 995-1018, November.
    16. T. Manouchehri & A. R. Nematollahi, 2019. "Periodic autoregressive models with closed skew-normal innovations," Computational Statistics, Springer, vol. 34(3), pages 1183-1213, September.
    17. Caporin, Massimiliano & Preś, Juliusz, 2012. "Modelling and forecasting wind speed intensity for weather risk management," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3459-3476.
    18. Soumya Das & Marc G. Genton & Yasser M. Alshehri & Georgiy L. Stenchikov, 2021. "A cyclostationary model for temporal forecasting and simulation of solar global horizontal irradiance," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    19. Mohammad Reza Mahmoudi & Mohsen Maleki, 2017. "A new method to detect periodically correlated structure," Computational Statistics, Springer, vol. 32(4), pages 1569-1581, December.
    20. Sarnaglia, A.J.Q. & Reisen, V.A. & Lévy-Leduc, C., 2010. "Robust estimation of periodic autoregressive processes in the presence of additive outliers," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2168-2183, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:99:y:2008:i:1:p:94-116. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.