IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v34y1997i4p365-372.html
   My bibliography  Save this article

A note on the ergodicity of non-linear autoregressive model

Author

Listed:
  • An, H. Z.
  • Chen, S. G.

Abstract

We examine the Markov chain Xt = [Phi](Xt - 1) + [var epsilon]tb, where Xt = (xt, ..., xt - p + 1)[tau], B = (1, 0, ..., 0)[tau]. Under some appropriate conditions on [Phi], we show the ergodicity for {Xt} when E[var epsilon]t2 is suitable small, and the geometric ergodicity when Ee[var epsilon]t is suitably small.

Suggested Citation

  • An, H. Z. & Chen, S. G., 1997. "A note on the ergodicity of non-linear autoregressive model," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 365-372, June.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:4:p:365-372
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(96)00204-0
    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. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
    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. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR‐GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
    2. Lee, O. & Shin, D.W., 2007. "A note on geometric ergodicity of a multiple threshold AR(1) processes on the boundary region with application to integrated m-m processes," Economics Letters, Elsevier, vol. 96(2), pages 226-231, August.
    3. Fonseca Giovanni, 2004. "On the Stationarity of First-order Nonlinear Time Series Models: Some Developments," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-9, May.
    4. Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2015. "Structure and asymptotic theory for nonlinear models with GARCH erros," Economia, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics], vol. 16(1), pages 1-21.
    5. Lee, Oesook, 2000. "On probabilistic properties of nonlinear ARMA(p,q) models," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 121-131, January.
    6. Harvill, Jane L. & Ray, Bonnie K., 2006. "Functional coefficient autoregressive models for vector time series," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3547-3566, August.
    7. Hwang, S. Y. & Woo, Mi-Ja, 2001. "Threshold ARCH(1) processes: asymptotic inference," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 11-20, May.

    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. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR‐GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
    2. Rydlewski, Jerzy P. & Snarska, Małgorzata, 2014. "On geometric ergodicity of skewed—SVCHARME models," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 192-197.
    3. repec:lan:wpaper:2374 is not listed on IDEAS
    4. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    5. repec:lan:wpaper:2372 is not listed on IDEAS
    6. Jean‐Pierre Stockis & Jürgen Franke & Joseph Tadjuidje Kamgaing, 2010. "On geometric ergodicity of CHARME models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 141-152, May.
    7. Felix Chan & Michael McAleer & Marcelo C. Medeiros, 2015. "Structure and asymptotic theory for nonlinear models with GARCH erros," Economia, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics], vol. 16(1), pages 1-21.
    8. Lu, Zudi & Jiang, Zhenyu, 2001. "L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 121-130, January.
    9. Lee, Oesook & Shin, Dong Wan, 2000. "On geometric ergodicity of the MTAR process," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 229-237, July.
    10. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. S. Valère Bitseki Penda & Adélaïde Olivier, 2017. "Autoregressive functions estimation in nonlinear bifurcating autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 179-210, July.
    12. repec:lan:wpaper:2453 is not listed on IDEAS
    13. Lee, Oesook, 2000. "On probabilistic properties of nonlinear ARMA(p,q) models," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 121-131, January.
    14. repec:lan:wpaper:2595 is not listed on IDEAS
    15. Lee, Chanho, 1998. "Asymptotics of a class of pth-order nonlinear autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 171-177, September.
    16. Hernández-Lerma, Onésimo & Lasserre, Jean B., 1996. "Existence of bounded invariant probability densities for Markov chains," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 359-366, August.
    17. Enwen Zhu & Jiezhong Zou & Zhenting Hou, 2007. "Analysis on adjoint non-recurrent property of nonlinear time series in random environment domain," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 353-360, April.
    18. Isao Ishida & Virmantas Kvedaras, 2015. "Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity," Econometrics, MDPI, vol. 3(1), pages 1-53, January.
    19. Carrasco, Marine, 2002. "Misspecified Structural Change, Threshold, and Markov-switching models," Journal of Econometrics, Elsevier, vol. 109(2), pages 239-273, August.
    20. Arash Nademi & Rahman Farnoosh, 2014. "Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(2), pages 275-293, February.
    21. Eckhard Liebscher, 2005. "Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 669-689, September.
    22. I A Venetis & I Paya & D Peel, 2009. "ESTAR model with multiple fixed points. Testing and Estimation," Working Papers 599093, Lancaster University Management School, Economics Department.
    23. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2009. "Estimators for alternating nonlinear autoregression," Journal of Multivariate Analysis, Elsevier, vol. 100(2), pages 266-277, February.
    24. Joseph Tadjuidje Kamgaing & Hernando Ombao & Richard A. Davis, 2009. "Autoregressive processes with data‐driven regime switching," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 505-533, September.

    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:34:y:1997:i:4:p:365-372. 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.