IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v8y2004i2n12.html
   My bibliography  Save this article

On the Stationarity of First-order Nonlinear Time Series Models: Some Developments

Author

Listed:
  • Fonseca Giovanni

    (University of Insubria Varese)

Abstract

In the present paper we consider the general class of first-order nonlinear models. The main contributions concern primerly a generalization of the conditions for geometric ergodicity presented in Ferrante et al. (2003). The obtained result is then applied to two classes of first-order nonlinear models not previously addressed. Secondly we apply to general firstorder nonlinear models some recently developed conditions for the existence of the invariant measure of a Markov process. For this class of nonlinear models we also prove that the usual drift-condition for geometric ergodicity for Markov chains still holds even in the presence of an alternative assumption than T-continuity.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:sndecm:v:8:y:2004:i:2:n:12
    DOI: 10.2202/1558-3708.1216
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1558-3708.1216
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1558-3708.1216?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
    ---><---

    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. Tweedie, Richard L., 1975. "Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space," Stochastic Processes and their Applications, Elsevier, vol. 3(4), pages 385-403, October.
    2. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    3. 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.
    4. Cline, Daren B. H. & Pu, Huay-min H., 1998. "Verifying irreducibility and continuity of a nonlinear time series," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 139-148, September.
    5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, 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. Tue Gørgens & Christopher L. Skeels & Allan H. Würtz, 2009. "Efficient Estimation of Non-Linear Dynamic Panel Data Models with Application to Smooth Transition Models," CREATES Research Papers 2009-51, Department of Economics and Business Economics, Aarhus University.

    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. Shively, Gerald E., 2001. "Price thresholds, price volatility, and the private costs of investment in a developing country grain market," Economic Modelling, Elsevier, vol. 18(3), pages 399-414, August.
    2. 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.
    3. Erie Febrian & Aldrin Herwany, 2009. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Economics and Development Studies (WoPEDS) 200911, Department of Economics, Padjadjaran University, revised Sep 2009.
    4. Altaf Muhammad & Zhang Shuguang, 2015. "Impact Of Structural Shifts on Variance Persistence in Asymmetric Garch Models: Evidence From Emerging Asian and European Markets," Romanian Statistical Review, Romanian Statistical Review, vol. 63(1), pages 57-70, March.
    5. Ding, Jing & Jiang, Lei & Liu, Xiaohui & Peng, Liang, 2023. "Nonparametric tests for market timing ability using daily mutual fund returns," Journal of Economic Dynamics and Control, Elsevier, vol. 150(C).
    6. Zou, Yongjie & Li, Honggang, 2014. "Time spans between price maxima and price minima in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 303-309.
    7. Gerard H. Kuper & Daan P. van Soest, 2006. "Does Oil Price Uncertainty Affect Energy Use?," The Energy Journal, , vol. 27(1), pages 55-78, January.
    8. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
    9. Dominique Guegan, 2005. "How can we Define the Concept of Long Memory? An Econometric Survey," Econometric Reviews, Taylor & Francis Journals, vol. 24(2), pages 113-149.
    10. Harry-Paul Vander Elst, 2015. "FloGARCH: Realizing Long Memory and Asymmetries in Returns Valitility," Working Papers ECARES ECARES 2015-12, ULB -- Universite Libre de Bruxelles.
    11. Charles, Amélie, 2010. "The day-of-the-week effects on the volatility: The role of the asymmetry," European Journal of Operational Research, Elsevier, vol. 202(1), pages 143-152, April.
    12. Theodore Panagiotidis, 2010. "Market efficiency and the Euro: the case of the Athens stock exchange," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 37(3), pages 237-251, July.
    13. Bachar Fakhry & Christian Richter, 2018. "Does the Federal Constitutional Court Ruling Mean the German Financial Market is Efficient?," European Journal of Business Science and Technology, Mendel University in Brno, Faculty of Business and Economics, vol. 4(2), pages 111-125.
    14. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    15. Ender Su & John Bilson, 2011. "Trading asymmetric trend and volatility by leverage trend GARCH in Taiwan stock index," Applied Economics, Taylor & Francis Journals, vol. 43(26), pages 3891-3905.
    16. Chuong Luong & Nikolai Dokuchaev, 2018. "Forecasting of Realised Volatility with the Random Forests Algorithm," JRFM, MDPI, vol. 11(4), pages 1-15, October.
    17. Alistair Mees & Berndt Pilgram, 2000. "Non-Linear Markov Modelling Using Canonical Variate Analysis: Forecasting Exchange Rate Volatility," Econometric Society World Congress 2000 Contributed Papers 1162, Econometric Society.
    18. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    19. Henryk Gurgul & Robert Syrek, 2023. "Contagion between selected European indexes during the Covid-19 pandemic," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(1), pages 47-59.
    20. Serge Darolles & Jeremy Dudek & Gaëlle Le Fol, 2012. "Liquidity Contagion. The Emerging Sovereign Debt Markets example," Post-Print hal-01632803, HAL.

    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:bpj:sndecm:v:8:y:2004:i:2:n:12. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.