IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v31y1997i3p213-224.html
   My bibliography  Save this article

The geometric ergodicity and existence of moments for a class of non-linear time series model

Author

Listed:
  • An, Hongzhi
  • Chen, Min
  • Huang, Fuchun

Abstract

In this paper we consider the non-linear time series model xt=[var epsilon]t([alpha]0+[alpha]1xt-1r[beta]+...+[alpha]pxt-pr[beta])1/r. When r = 2 it is called the [beta]-ARCH(p) model. We examine the geometric ergodicity and the existence of higher-order moments for this model.

Suggested Citation

  • An, Hongzhi & Chen, Min & Huang, Fuchun, 1997. "The geometric ergodicity and existence of moments for a class of non-linear time series model," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 213-224, January.
    • Handle: RePEc:eee:stapro:v:31:y:1997:i:3:p:213-224
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(96)00033-8
    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. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    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. Janusz Kawczak & Reg Kulperger & Hao Yu, 2005. "The empirical distribution function and partial sum process of residuals from a stationary arch with drift process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 747-765, December.
    2. Frédérique Bec & Anders Rahbek, 2004. "Vector equilibrium correction models with non-linear discontinuous adjustments," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 628-651, December.
    3. Laïb, Naâmane & Lounis, Tewfik, 2021. "Asymptotically optimal tests for non-linear autoregressive model with β-ARCH errors," Statistics & Probability Letters, Elsevier, vol. 178(C).
    4. Hwang, S. Y. & Woo, Mi-Ja, 2001. "Threshold ARCH(1) processes: asymptotic inference," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 11-20, May.
    5. Hwang, S. Y. & Kim, Tae Yoon, 2004. "Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 295-314, April.
    6. Carvalho, Alexandre & Skoulakis, Georgios, 2005. "Ergodicity and existence of moments for local mixtures of linear autoregressions," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 313-322, March.

    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. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    2. Corbet, Shaen & Larkin, Charles & McMullan, Caroline, 2020. "The impact of industrial incidents on stock market volatility," Research in International Business and Finance, Elsevier, vol. 52(C).
    3. 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.
    4. P. Kearns & A.R. Pagan, 1993. "Australian Stock Market Volatility: 1875–1987," The Economic Record, The Economic Society of Australia, vol. 69(2), pages 163-178, June.
    5. Conrad, Christian & Mammen, Enno, 2016. "Asymptotics for parametric GARCH-in-Mean models," Journal of Econometrics, Elsevier, vol. 194(2), pages 319-329.
    6. Andrea Bucci, 2020. "Realized Volatility Forecasting with Neural Networks," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 502-531.
    7. Jon Michel, 2020. "The Limiting Distribution of a Non‐Stationary Integer Valued GARCH(1,1) Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 351-356, March.
    8. Oliver Linton & Dajing Shang & Yang Yan, 2012. "Efficient estimation of conditional risk measures in a semiparametric GARCH model," CeMMAP working papers 25/12, Institute for Fiscal Studies.
    9. 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.
    10. McMillan, David G. & Speight, Alan E. H., 2001. "Non-ferrous metals price volatility: a component analysis," Resources Policy, Elsevier, vol. 27(3), pages 199-207, September.
    11. Nikolaos Kourogenis & Nikitas Pittis, 2008. "Testing for a unit root under errors with just barely infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1066-1087, November.
    12. William Miles, 2011. "Long-Range Dependence in U.S. Home Price Volatility," The Journal of Real Estate Finance and Economics, Springer, vol. 42(3), pages 329-347, April.
    13. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
    14. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    15. Behmiri, Niaz Bashiri & Manera, Matteo, 2015. "The role of outliers and oil price shocks on volatility of metal prices," Resources Policy, Elsevier, vol. 46(P2), pages 139-150.
    16. Oliver Linton & Douglas Steigerwald, 2000. "Adaptive testing in arch models," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 145-174.
    17. Storti, G., 2006. "Minimum distance estimation of GARCH(1,1) models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1803-1821, December.
    18. Trapero, Juan R. & Cardós, Manuel & Kourentzes, Nikolaos, 2019. "Empirical safety stock estimation based on kernel and GARCH models," Omega, Elsevier, vol. 84(C), pages 199-211.
    19. LINTON, Olivier & PERRON, Benoît, 1999. "The Shape of the Risk Premium: Evidence from a Semiparametric Garch Model," Cahiers de recherche 9911, Universite de Montreal, Departement de sciences economiques.
    20. David McMillan & Alan Speight, 2006. "Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market," Applied Financial Economics, Taylor & Francis Journals, vol. 16(13), pages 959-972.

    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:31:y:1997:i:3:p:213-224. 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.