IDEAS home Printed from https://ideas.repec.org/p/rim/rimwps/18-25.html
   My bibliography  Save this paper

Mildly explosive autoregression under stationary conditional heteroskedasticity

Author

Listed:
  • Stelios Arvanitis

    (Athens University of Economics and Business, Greece)

  • Tassos Magdalinos

    (University of Southampton, UK; Rimini Centre for Economic Analysis)

Abstract

A limit theory is developed for mildly explosive autoregressions under stationary (weakly or strongly dependent) conditionally heteroskedastic errors. The conditional variance process is allowed to be stationary, integrable and mixingale, thus encompassing general classes of GARCH type or stochastic volatility models. No mixing conditions nor moments of higher order than 2 are assumed for the innovation process. As in Magdalinos (2012), we find that the asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the form of the limiting distribution and, in the case of long range dependence, the rate of convergence, while conditional heteroskedasticity affects only the asymptotic variance. These effects are cancelled out in least squares regression theory and thereby the Cauchy limit theory of Phillips and Magdalinos (2007a) remains invariant to a wide class of stationary conditionally heteroskedastic innovations processes.

Suggested Citation

  • Stelios Arvanitis & Tassos Magdalinos, 2018. "Mildly explosive autoregression under stationary conditional heteroskedasticity," Working Paper series 18-25, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:18-25
    as

    Download full text from publisher

    File URL: http://rcea.org/RePEc/pdf/wp18-25.pdf
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    2. Gangzheng Guo & Yixiao Sun & Shaoping Wang, 2019. "Testing for moderate explosiveness," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 73-95.
    3. Ovidijus Stauskas, 2020. "On the limit theory of mixed to unity VARs: Panel setting with weakly dependent errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 892-898, November.
    4. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    5. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic theory for rough fractional Vasicek models," Economics Letters, Elsevier, vol. 177(C), pages 26-29.
    6. Anton Skrobotov, 2022. "Testing for explosive bubbles: a review," Papers 2207.08249, arXiv.org.
    7. Yiu Lim Lui & Weilin Xiao & Jun Yu, 2021. "Mildly Explosive Autoregression with Anti‐persistent Errors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(2), pages 518-539, April.
    8. Stauskas, Ovidijus, 2019. "On the Limit Theory of Mixed to Unity VARs: Panel Setting With Weakly Dependent Errors," Working Papers 2019:2, Lund University, Department of Economics.
    9. Jingjie Xiang & Gangzheng Guo & Qing Zhao, 2022. "Testing for a Moderately Explosive Process with Structural Change in Drift," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(2), pages 300-333, April.

    More about this item

    Keywords

    Central limit theory; Explosive autoregression; Long Memory; Conditional heteroskedasticity; GARCH; mixingale; Cauchy distribution;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:rim:rimwps:18-25. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Marco Savioli (email available below). General contact details of provider: https://edirc.repec.org/data/rcfeait.html .

    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.