IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v26y2005i4p489-518.html
   My bibliography  Save this article

Parameter Estimation for Periodically Stationary Time Series

Author

Listed:
  • Paul L. Anderson
  • Mark M. Meerschaert

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 innovations have a finite fourth moment. These asymptotic results are useful to determine which model parameters are significant. In the process, we also develop asymptotics for the Yule–Walker estimates.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:4:p:489-518
    DOI: 10.1111/j.1467-9892.2005.00428.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2005.00428.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2005.00428.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Taylan A. Ula, 1993. "Forecasting Of Multivariate Periodic Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(6), pages 645-657, November.
    3. P. L. Anderson & A. V. Vecchia, 1993. "Asymptotic Results For Periodic Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(1), pages 1-18, January.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. K. Triantafyllopoulos & G. Montana, 2011. "Dynamic modeling of mean-reverting spreads for statistical arbitrage," Computational Management Science, Springer, vol. 8(1), pages 23-49, April.
    4. K. Triantafyllopoulos, 2007. "Covariance estimation for multivariate conditionally Gaussian dynamic linear models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(8), pages 551-569.
    5. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    6. Mohammad Reza Mahmoudi & Mohsen Maleki, 2017. "A new method to detect periodically correlated structure," Computational Statistics, Springer, vol. 32(4), pages 1569-1581, December.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Triantafyllopoulos, K. & Nason, G.P., 2007. "A Bayesian analysis of moving average processes with time-varying parameters," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1025-1046, October.

    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. 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.
    3. Daniel Dzikowski & Carsten Jentsch, 2024. "Structural Periodic Vector Autoregressions," Papers 2401.14545, arXiv.org.
    4. 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.
    5. 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.
    6. Choi, In & Kurozumi, Eiji, 2012. "Model selection criteria for the leads-and-lags cointegrating regression," Journal of Econometrics, Elsevier, vol. 169(2), pages 224-238.
    7. Lee, Yoon-Jin & Okui, Ryo & Shintani, Mototsugu, 2018. "Asymptotic inference for dynamic panel estimators of infinite order autoregressive processes," Journal of Econometrics, Elsevier, vol. 204(2), pages 147-158.
    8. McKenzie, C.R., 1997. "The properties of some two step estimators of ARMA Models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(3), pages 451-456.
    9. Zacharias Psaradakis & Marián Vávra, 2019. "Portmanteau tests for linearity of stationary time series," Econometric Reviews, Taylor & Francis Journals, vol. 38(2), pages 248-262, February.
    10. Demetrescu, Matei & Salish, Nazarii, 2024. "(Structural) VAR models with ignored changes in mean and volatility," International Journal of Forecasting, Elsevier, vol. 40(2), pages 840-854.
    11. Bunzel, Helle, 2006. "FIXED-b ASYMPTOTICS IN SINGLE-EQUATION COINTEGRATION MODELS WITH ENDOGENOUS REGRESSORS," Econometric Theory, Cambridge University Press, vol. 22(4), pages 743-755, August.
    12. DUFOUR, Jean-Marie & TAREK, Jouini, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 2005-09, Universite de Montreal, Departement de sciences economiques.
    13. Oscar Jorda & Sharon Kozicki, 2007. "Estimation and Inference by the Method of Projection Minimum Distance," Working Papers 148, University of California, Davis, Department of Economics.
    14. Hafner, Christian M. & Linton, Oliver B. & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," Journal of Econometrics, Elsevier, vol. 217(2), pages 431-470.
    15. 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.
    16. Oscar Jorda & Alan Taylor & Sanjay Singh, 2019. "The Long-Run Effects of Monetary Policy," 2019 Meeting Papers 1307, Society for Economic Dynamics.
    17. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    18. Domenico Cucina & Manuel Rizzo & Eugen Ursu, 2018. "Identification of multiregime periodic autotregressive models by genetic algorithms," Post-Print hal-03187870, HAL.
    19. Oscar Jorda, 2007. "Inference for Impulse Responses," Working Papers 201, University of California, Davis, Department of Economics.
    20. Richard T. Baillie & Dooyeon Cho & Seunghwa Rho, 2023. "Approximating long-memory processes with low-order autoregressions: Implications for modeling realized volatility," Empirical Economics, Springer, vol. 64(6), pages 2911-2937, June.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jtsera:v:26:y:2005:i:4:p:489-518. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.