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Sign-Based Unit Root Tests For Explosive Financial Bubbles In The Presence Of Deterministically Time-Varying Volatility

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

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 sign-based variant of the Phillips, Shi, and Yu (2015, International Economic Review 56, 1043–1077) test. Unlike the original test, the sign-based test does not require bootstrap-type methods to control size in the presence of time-varying volatility. Under a locally explosive alternative, the sign-based test delivers higher power than the original test for many time-varying volatility and bubble specifications. However, since the original test can still outperform the sign-based one for some specifications, we also propose a union of rejections procedure that combines the original and sign-based tests, employing a wild bootstrap to control size. This is shown to capture most of the power available from the better performing of the two tests. We also show how a sign-based statistic can be used to date the bubble start and end points. An empirical illustration using Bitcoin price data is provided.

Suggested Citation

  • Harvey, David I. & Leybourne, Stephen J. & Zu, Yang, 2020. "Sign-Based Unit Root Tests For Explosive Financial Bubbles In The Presence Of Deterministically Time-Varying Volatility," Econometric Theory, Cambridge University Press, vol. 36(1), pages 122-169, February.
    • Handle: RePEc:cup:etheor:v:36:y:2020:i:1:p:122-169_4
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    Cited by:

    1. Jean-Louis Bago & Koffi Akakpo & Imad Rherrad & Ernest Ouédraogo, 2021. "Volatility Spillover and International Contagion of Housing Bubbles," JRFM, MDPI, vol. 14(7), pages 1-14, June.
    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. H. Peter Boswijk & Jun Yu & Yang Zu, 2024. "Testing for an Explosive Bubble using High-Frequency Volatility," Working Papers 202402, University of Macau, Faculty of Business Administration.
    4. Feng, Hao, 2023. "Testing for explosive bubbles in the presence of non-Gaussian conditions," Economics Letters, Elsevier, vol. 233(C).
    5. 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.
    6. Aktham Maghyereh & Hussein Abdoh, 2022. "Can news-based economic sentiment predict bubbles in precious metal markets?," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-29, December.
    7. 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).
    8. Eiji Kurozumi & Anton Skrobotov & Alexey Tsarev, 2020. "Time-Transformed Test for the Explosive Bubbles under Non-stationary Volatility," Papers 2012.13937, arXiv.org, revised Nov 2021.
    9. Eiji Kurozumi & Anton Skrobotov, 2023. "Improving the accuracy of bubble date estimators under time-varying volatility," Papers 2306.02977, arXiv.org.
    10. Nicole Branger & Mark Trede & Bernd Wilfling, 2024. "Extracting stock-market bubbles from dividend futures," CQE Working Papers 10724, Center for Quantitative Economics (CQE), University of Muenster.
    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," Journal of Financial Econometrics, Oxford University Press, 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.
    13. Shuping Shi & Peter C. B. Phillips, 2022. "Econometric Analysis of Asset Price Bubbles," Cowles Foundation Discussion Papers 2331, Cowles Foundation for Research in Economics, Yale University.

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