IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v66y1998i1p1-21.html
   My bibliography  Save this article

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

Author

Listed:
  • Bentarzi, Mohamed

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.

Suggested Citation

  • Bentarzi, Mohamed, 1998. "Model-Building Problem of Periodically Correlatedm-Variate Moving Average Processes," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 1-21, July.
    • Handle: RePEc:eee:jmvana:v:66:y:1998:i:1:p:1-21
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(97)91733-4
    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. 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.
    2. Marc Hallin, 1984. "Spectral factorization of nonstationary moving average processes," ULB Institutional Repository 2013/2001, ULB -- Universite Libre de Bruxelles.
    3. Bentarzi, Mohamed & Hallin, Marc, 1996. "Locally Optimal Tests against Periodic Autoregression: Parametric and Nonparametric Approaches," Econometric Theory, Cambridge University Press, vol. 12(1), pages 88-112, March.
    4. Mohamed Bentarzi & Marc Hallin, 1994. "On The Invertibility Of Periodic Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 263-268, May.
    5. Marc Hallin & Mohamed Bentarzi, 1998. "Spectral factorization of periodically correlated MA(1) processes," ULB Institutional Repository 2013/2073, ULB -- Universite Libre de Bruxelles.
    6. 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.
    7. 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.
    8. 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.
    9. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, 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. 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.
    2. Aknouche, Abdelhakim & Bentarzi, Mohamed, 2008. "On the existence of higher-order moments of periodic GARCH models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3262-3268, December.

    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. Łukasz Lenart, 2017. "Examination of Seasonal Volatility in HICP for Baltic Region Countries: Non-Parametric Test versus Forecasting Experiment," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(1), pages 29-67, March.
    2. Politis, Dimitris, 2016. "HEGY test under seasonal heterogeneity," University of California at San Diego, Economics Working Paper Series qt2q4054kf, Department of Economics, UC San Diego.
    3. Pami Dua & Lokendra Kumawat, 2005. "Modelling and Forecasting Seasonality in Indian Macroeconomic Time Series," Working papers 136, Centre for Development Economics, Delhi School of Economics.
    4. Peter Boswijk, H. & Franses, Philip Hans, 1995. "Testing for periodic integration," Economics Letters, Elsevier, vol. 48(3-4), pages 241-248, June.
    5. Alexander Vosseler & Enzo Weber, 2018. "Forecasting seasonal time series data: a Bayesian model averaging approach," Computational Statistics, Springer, vol. 33(4), pages 1733-1765, December.
    6. Franses, Philip Hans & Boswijk, H. Peter, 1996. "Temporal aggregation in a periodically integrated autoregressive process," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 235-240, October.
    7. 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.
    8. Eiji Kurozumi, 2002. "Testing For Periodic Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 243-270.
    9. 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.
    10. Richard M. Todd, 1989. "Periodic linear-quadratic methods for modeling seasonality," Staff Report 127, Federal Reserve Bank of Minneapolis.
    11. Tomas Barrio Castro & Mariam Camarero & Cecilio Tamarit, 2015. "An analysis of the trade balance for OECD countries using periodic integration and cointegration," Empirical Economics, Springer, vol. 49(2), pages 389-402, September.
    12. 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.
    13. Zou, Nan & Politis, Dimitris N., 2021. "Bootstrap seasonal unit root test under periodic variation," Econometrics and Statistics, Elsevier, vol. 19(C), pages 1-21.
    14. Basawa, I. V. & Lund, Robert & Shao, Qin, 2004. "First-order seasonal autoregressive processes with periodically varying parameters," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 299-306, May.
    15. del Barrio Castro, Tomás & Osborn, Denise R., 2008. "Cointegration For Periodically Integrated Processes," Econometric Theory, Cambridge University Press, vol. 24(1), pages 109-142, February.
    16. Paulo M.M. Rodrigues & Pedro M.D.C.B. Gouveia, 2004. "An Application of PAR Models for Tourism Forecasting," Tourism Economics, , vol. 10(3), pages 281-303, September.
    17. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    18. Tomás Barrio & Mariam Camarero & Cecilio Tamarit, 2019. "Testing for Periodic Integration with a Changing Mean," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 45-75, June.
    19. 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.
    20. Lenart, Łukasz, 2013. "Non-parametric frequency identification and estimation in mean function for almost periodically correlated time series," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 252-269.

    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:66:y:1998:i:1:p:1-21. 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.