IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v42y2021i3p314-337.html
   My bibliography  Save this article

Asymptotic Behavior of Delay Times of Bubble Monitoring Tests

Author

Listed:
  • Eiji Kurozumi

Abstract

We investigate the asymptotic properties of the stopping times based on the monitoring tests for a bubble, that is, ADF‐type and CUSUM‐type tests. We derive the stochastic orders of these stopping times and find that they depend on the relative position of the emerging date of a bubble. We show that when a bubble emerges early in the monitoring period, the diverging rate of the stopping time based on the CUSUM‐type detector is slower than that based on the ADF‐type detector, which implies that the former tends to find a bubble earlier than the latter, whereas this advantage disappears for the late emerging bubble. We also derive the limiting distribution of the stopping time based on the CUSUM detector. The finite sample simulations support the theoretical result.

Suggested Citation

  • Eiji Kurozumi, 2021. "Asymptotic Behavior of Delay Times of Bubble Monitoring Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 314-337, May.
    • Handle: RePEc:bla:jtsera:v:42:y:2021:i:3:p:314-337
    DOI: 10.1111/jtsa.12569
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/jtsa.12569
    Download Restriction: no
    File URL: https://libkey.io/10.1111/jtsa.12569?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
    2. David I. Harvey & Stephen J. Leybourne & Robert Sollis, 2015. "Recursive Right-Tailed Unit Root Tests for an Explosive Asset Price Bubble," Journal of Financial Econometrics, Oxford University Press, vol. 13(1), pages 166-187.
    3. 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.
    4. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Limit Theory Of Real‐Time Detectors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1079-1134, November.
    5. Alexander Aue & Lajos Horváth & Marie Hušková & Piotr Kokoszka, 2006. "Change-point monitoring in linear models," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 373-403, November.
    6. Aue, Alexander & Horváth, Lajos & Reimherr, Matthew L., 2009. "Delay times of sequential procedures for multiple time series regression models," Journal of Econometrics, Elsevier, vol. 149(2), pages 174-190, April.
    7. Sam Astill & David I. Harvey & Stephen J. Leybourne & Robert Sollis & A. M. Robert Taylor, 2018. "Real‐Time Monitoring for Explosive Financial Bubbles," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 863-891, November.
    8. Diba, Behzad T & Grossman, Herschel I, 1988. "Explosive Rational Bubbles in Stock Prices?," American Economic Review, American Economic Association, vol. 78(3), pages 520-530, June.
    9. Phillips, Peter C.B. & Shi, Shu-Ping, 2018. "Financial Bubble Implosion And Reverse Regression," Econometric Theory, Cambridge University Press, vol. 34(4), pages 705-753, August.
    10. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1043-1078, November.
    11. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Limit Theory Of Real‐Time Detectors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1079-1134, November.
    12. Aue, Alexander & Horváth, Lajos, 2004. "Delay time in sequential detection of change," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 221-231, April.
    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. 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. Vicente Esteve & María A. Prats, 2021. "Financial bubbles and sustainability of public debt: The case of Spain," Working Papers 2111, Department of Applied Economics II, Universidad de Valencia.
    3. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    4. Vicente Esteve & María A. Prats, 2021. "Testing for rational bubbles in Australian housing market from a long-term perspective," Working Papers 2113, Department of Applied Economics II, Universidad de Valencia.
    5. Esteve Vicente & Prats Maria A., 2021. "Structural Breaks and Explosive Behavior in the Long-Run: The Case of Australian Real House Prices, 1870–2020," Economics - The Open-Access, Open-Assessment Journal, De Gruyter, vol. 15(1), pages 72-84, January.
    6. Emilio Congregado & Silviano Carmen Díaz-Roldán & Vicente Esteve, 2023. "Deficit sustainability and the Fiscal Theory of the Price Level: the case of Italy, 1861-2020," Working Papers 2301, Department of Applied Economics II, Universidad de Valencia.

    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. Wang, Xichen & Yan, Ji (Karena) & Yan, Cheng & Gozgor, Giray, 2021. "Emerging stock market exuberance and international short-term flows," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    2. 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.
    3. Gomis-Porqueras, Pedro & Shi, Shuping & Tan, David, 2022. "Gold as a financial instrument," Journal of Commodity Markets, Elsevier, vol. 27(C).
    4. Shuping Shi & Arafat Rahman & Ben Zhe Wang, 2020. "Australian Housing Market Booms: Fundamentals or Speculation?☆," The Economic Record, The Economic Society of Australia, vol. 96(315), pages 381-401, December.
    5. Moreira, Afonso M. & Martins, Luis F., 2020. "A new mechanism for anticipating price exuberance," International Review of Economics & Finance, Elsevier, vol. 65(C), pages 199-221.
    6. 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).
    7. Gharib, Cheima & Mefteh-Wali, Salma & Serret, Vanessa & Ben Jabeur, Sami, 2021. "Impact of COVID-19 pandemic on crude oil prices: Evidence from Econophysics approach," Resources Policy, Elsevier, vol. 74(C).
    8. Janusz Sobieraj & Dominik Metelski, 2021. "Testing Housing Markets for Episodes of Exuberance: Evidence from Different Polish Cities," JRFM, MDPI, vol. 14(9), pages 1-29, September.
    9. Caravello, Tomas E. & Psaradakis, Zacharias & Sola, Martin, 2023. "Rational bubbles: Too many to be true?," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    10. Jalan, Akanksha & Matkovskyy, Roman & Potì, Valerio, 2022. "Shall the winning last? A study of recent bubbles and persistence," Finance Research Letters, Elsevier, vol. 45(C).
    11. Yu, Lu & Li, Yanglin, 2023. "Testing factor models when asset bubbles occur: A time-varying perspective," Economic Modelling, Elsevier, vol. 124(C).
    12. Akcora, Begum & Kandemir Kocaaslan, Ozge, 2023. "Price bubbles in the European natural gas market between 2011 and 2020," Resources Policy, Elsevier, vol. 80(C).
    13. Aktham Maghyereh & Hussein Abdoh, 2022. "Bubble contagion effect between the main precious metals," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 40(1), pages 43-63, March.
    14. Yang, Hui & Ferrer, Román, 2023. "Explosive behavior in the Chinese stock market: A sectoral analysis," Pacific-Basin Finance Journal, Elsevier, vol. 81(C).
    15. 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.
    16. Pang, Tianxiao & Du, Lingjie & Chong, Terence Tai-Leung, 2021. "Estimating multiple breaks in nonstationary autoregressive models," Journal of Econometrics, Elsevier, vol. 221(1), pages 277-311.
    17. Astill, Sam & Taylor, A.M. Robert & Kellard, Neil & Korkos, Ioannis, 2023. "Using covariates to improve the efficacy of univariate bubble detection methods," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 342-366.
    18. Bogdan, Dima & Ştefana Maria, Dima & Roxana, Ioan, 2022. "A Value-at-Risk forecastability indicator in the framework of a Generalized Autoregressive Score with “Asymmetric Laplace Distribution”," Finance Research Letters, Elsevier, vol. 45(C).
    19. Ajmi, Ahdi Noomen & Hammoudeh, Shawkat & Mokni, Khaled, 2021. "Detection of bubbles in WTI, brent, and Dubai oil prices: A novel double recursive algorithm," Resources Policy, Elsevier, vol. 70(C).
    20. Bellón, Carlos & Figuerola-Ferretti, Isabel, 2022. "Bubbles in Ethereum," Finance Research Letters, Elsevier, vol. 46(PB).

    More about this item

    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:bla:jtsera:v:42:y:2021:i:3:p:314-337. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.