IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i1p79-87.html
   My bibliography  Save this article

On stationarity and [beta]-mixing of periodic bilinear processes

Author

Listed:
  • Bibi, Abdelouahab
  • Lessak, Radia

Abstract

This paper studies some probabilistic properties of periodic bilinear processes. In these nonlinear models, the parameters are allowed to switch between different regimes. Stationarity and geometric ergodicity conditions (in periodic sense) are given under general and tractable assumptions. We use these results to give necessary and sufficient conditions for stationarity of specific periodic GARCH processes which can be written as a periodic bilinear models. Moreover, it is shown that local stationarity i.e., stationarity within each regime, is not necessary to obtain global stationarity.

Suggested Citation

  • Bibi, Abdelouahab & Lessak, Radia, 2009. "On stationarity and [beta]-mixing of periodic bilinear processes," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 79-87, January.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:1:p:79-87
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00348-9
    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. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549, Decembrie.
    2. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
    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. Abdelouahab Bibi & Ahmed Ghezal, 2016. "On periodic time-varying bilinear processes: structure and asymptotic inference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(3), pages 395-420, August.

    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 D. Feigin, 2020. "Correction to: Random Coefficient Autoregressive Processes: a Markov Chain Analysis of Stationarity and Finiteness of Moments by Paul D. Feigin and Richard L. Tweedie J. Time Series Anal., Vol. 6, No.," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 899-900, November.
    2. Franses, P.H. & McAleer, M., 1995. "Testing Nested and Non-Nested Periodically Integrated Autoregressive Models," Papers 9510, Tilburg - Center for Economic Research.
    3. Elizabeth Bucacos, 2008. "Real (effective) exchange rate in Uruguay: a periodic cointegration approach," Monetaria, CEMLA, vol. 0(2), pages 265-289, julio-sep.
    4. Jonathan Aylen & Kevin Albertson & Gina Cavan, 2014. "The impact of weather and climate on tourist demand: the case of Chester Zoo," Climatic Change, Springer, vol. 127(2), pages 183-197, November.
    5. Beenstock, Michael & Reingewertz, Yaniv & Paldor, Nathan, 2016. "Testing the historic tracking of climate models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1234-1246.
    6. Łukasz Lenart & Błażej Mazur, 2016. "On Bayesian Inference for Almost Periodic in Mean Autoregressive Models," FindEcon Chapters: Forecasting Financial Markets and Economic Decision-Making, in: Magdalena Osińska (ed.), Statistical Review, vol. 63, 2016, 3, edition 1, volume 63, chapter 1, pages 255-272, University of Lodz.
    7. 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.
    8. Man, K. S., 2004. "Linear prediction of temporal aggregates under model misspecification," International Journal of Forecasting, Elsevier, vol. 20(4), pages 659-670.
    9. A. Christian Silva & Ju-Yi Yen, 2010. "Stochastic resonance and the trade arrival rate of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 461-466.
    10. M. Angeles Carnero & Siem Jan Koopman & Marius Ooms, 2003. "Periodic Heteroskedastic RegARFIMA Models for Daily Electricity Spot Prices," Tinbergen Institute Discussion Papers 03-071/4, Tinbergen Institute.
    11. Artur Silva Lopes, 2006. "Deterministic seasonality in Dickey–Fuller tests: should we care?," Empirical Economics, Springer, vol. 31(1), pages 165-182, March.
    12. Aue, Alexander, 2004. "Strong approximation for RCA(1) time series with applications," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 369-382, July.
    13. Jentsch, Carsten & Subba Rao, Suhasini, 2015. "A test for second order stationarity of a multivariate time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 124-161.
    14. Olexa, Michal, 1999. "Analysis and Econometric Modelling of the Fiscal Sector in the Slovak Republic," Transition Economics Series 2, Institute for Advanced Studies.
    15. Melard, G. & Pasteels, J. -M., 2000. "Automatic ARIMA modeling including interventions, using time series expert software," International Journal of Forecasting, Elsevier, vol. 16(4), pages 497-508.
    16. Gabriel Pons Rotger, 2004. "Seasonal Unit Root Testing Based on the Temporal Aggregation of Seasonal Cycles," Economics Working Papers 2004-1, Department of Economics and Business Economics, Aarhus University.
    17. Hwang, S.Y. & Basawa, I.V., 2009. "Branching Markov processes and related asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1155-1167, July.
    18. Bradley Michael D. & Jansen Dennis W., 2000. "Are Business Cycle Dynamics the Same across Countries? Testing Linearity around the Globe," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(2), pages 1-23, July.
    19. Feike C. Drost & Ramon Van Den Akker & Bas J. M. Werker, 2008. "Local asymptotic normality and efficient estimation for INAR(p) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 783-801, September.
    20. Dennis Fok & Philip Hans Franses, 2013. "Testing earnings management," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(3), pages 281-292, August.

    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:eee:stapro:v:79:y:2009:i:1:p:79-87. 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.