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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
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    Cited by:

    1. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    2. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    3. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic theory for rough fractional Vasicek models," Economics Letters, Elsevier, vol. 177(C), pages 26-29.
    4. Anton Skrobotov, 2022. "Testing for explosive bubbles: a review," Papers 2207.08249, arXiv.org.
    5. 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.
    6. 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.
    7. 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.
    8. Gangzheng Guo & Yixiao Sun & Shaoping Wang, 2019. "Testing for moderate explosiveness," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 73-95.
    9. 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.

    More about this item

    Keywords

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

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