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Testing explosive bubbles with time-varying volatility

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  • David I. Harvey
  • Stephen J. Leybourne
  • Yang Zu

Abstract

This article considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a weighted least squares-based variant of the Phillips et al.) test for explosive autoregressive behavior. We find that such an approach has appealing asymptotic power properties, with the potential to deliver substantially greater power than the established OLS-based approach for many volatility and bubble settings. Given that the OLS-based test can outperform the weighted least squares-based test for other volatility and bubble specifications, we also suggest a union of rejections procedure that succeeds in capturing the better power available from the two constituent tests for a given alternative. Our approach involves a nonparametric kernel-based volatility function estimator for computation of the weighted least squares-based statistic, together with the use of a wild bootstrap procedure applied jointly to both individual tests, delivering a powerful testing procedure that is asymptotically size-robust to a wide range of time-varying volatility specifications.

Suggested Citation

  • David I. Harvey & Stephen J. Leybourne & Yang Zu, 2019. "Testing explosive bubbles with time-varying volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(10), pages 1131-1151, November.
  • Handle: RePEc:taf:emetrv:v:38:y:2019:i:10:p:1131-1151
    DOI: 10.1080/07474938.2018.1536099
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    2. Harvey, David I. & Leybourne, Stephen J. & Sollis, Robert & Taylor, A.M. Robert, 2016. "Tests for explosive financial bubbles in the presence of non-stationary volatility," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 548-574.
    3. Ke-Li Xu & Jui-Chung Yang, 2015. "Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Non-stationary Volatility," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 63-86, March.
    4. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    5. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(3), pages 587-636, June.
    6. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    7. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
    8. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
    9. Harvey, David I. & Leybourne, Stephen J. & Sollis, Robert, 2017. "Improving the accuracy of asset price bubble start and end date estimators," Journal of Empirical Finance, Elsevier, vol. 40(C), pages 121-138.
    10. Ke‐Li Xu, 2015. "Testing for structural change under non‐stationary variances," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 274-305, June.
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    Citations

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    Cited by:

    1. Yang Hu, 2023. "A review of Phillips‐type right‐tailed unit root bubble detection tests," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 141-158, February.
    2. Verena Monschang & Bernd Wilfling, 2021. "Sup-ADF-style bubble-detection methods under test," Empirical Economics, Springer, vol. 61(1), pages 145-172, July.
    3. Zhang, Erhua & Wu, Jilin, 2020. "Adaptive estimation of AR∞ models with time-varying variances," Economics Letters, Elsevier, vol. 197(C).
    4. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    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. Esteve, Vicente & Prats, María A., 2023. "Testing explosive bubbles with time-varying volatility: the case of Spanish public debt," LSE Research Online Documents on Economics 116980, London School of Economics and Political Science, LSE Library.
    7. Stefan Richter & Weining Wang & Wei Biao Wu, 2018. "A supreme test for periodic explosive GARCH," Papers 1812.03475, arXiv.org.
    8. Vicente Esteve & María A. Prats, 2022. "Testing explosive bubbles with time-varying volatility: The case of the Spanish public debt, 1850?2021," Working Papers 2205, Department of Applied Economics II, Universidad de Valencia.
    9. Esteve, Vicente & Prats, María A., 2023. "Testing explosive bubbles with time-varying volatility: The case of Spanish public debt," Finance Research Letters, Elsevier, vol. 51(C).
    10. Gil-Alana, Luis Alberiko & Dettoni, Robinson & Costamagna, Rodrigo & Valenzuela, Mario, 2019. "Rational bubbles in the real housing stock market: Empirical evidence from Santiago de Chile," Research in International Business and Finance, Elsevier, vol. 49(C), pages 269-281.
    11. Sam Astill & David I Harvey & Stephen J Leybourne & A M Robert Taylor & Yang Zu, 2023. "CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 21(1), pages 187-227.
    12. Xuanling Yang & Dong Li & Ting Zhang, 2024. "A simple stochastic nonlinear AR model with application to bubble," Papers 2401.07038, arXiv.org.

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