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A note on the Gumbel convergence for the Lee and Mykland jump tests

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  • Nunes, João Pedro Vidal
  • Ruas, João Pedro

Abstract

The Lee and Mykland (2008, 2012) nonparametric jump tests have been widely used in the literature but its critical region is stated with reference to the asymptotic distribution of the maximum of a set of standard normal variates. However, such reference would imply a typo (of a non-negligible order) for the norming constants adopted. By using the asymptotic distribution of the maximum of a set of folded normal random variables instead, this paper shows that there is no typo at all, thus preserving the validity of all the empirical findings based on these tests.

Suggested Citation

  • Nunes, João Pedro Vidal & Ruas, João Pedro, 2024. "A note on the Gumbel convergence for the Lee and Mykland jump tests," Finance Research Letters, Elsevier, vol. 59(C).
    • Handle: RePEc:eee:finlet:v:59:y:2024:i:c:s1544612323011868
    DOI: 10.1016/j.frl.2023.104814
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    References listed on IDEAS

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    1. Bibinger, Markus & Neely, Christopher & Winkelmann, Lars, 2019. "Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 158-184.
    2. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    3. Corsi, Fulvio & Pirino, Davide & Renò, Roberto, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Journal of Econometrics, Elsevier, vol. 159(2), pages 276-288, December.
    4. Daniel Bradley & Jonathan Clarke & Suzanne Lee & Chayawat Ornthanalai, 2014. "Are Analysts’ Recommendations Informative? Intraday Evidence on the Impact of Time Stamp Delays," Journal of Finance, American Finance Association, vol. 69(2), pages 645-673, April.
    5. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    6. Lee, Suzanne S. & Mykland, Per A., 2012. "Jumps in equilibrium prices and market microstructure noise," Journal of Econometrics, Elsevier, vol. 168(2), pages 396-406.
    7. Christian Palmes & Jeannette H. C. Woerner, 2016. "The Gumbel test and jumps in the volatility process," Statistical Inference for Stochastic Processes, Springer, vol. 19(2), pages 235-258, July.
    8. Schneider, Paul & Sögner, Leopold & Veža, Tanja, 2010. "The Economic Role of Jumps and Recovery Rates in the Market for Corporate Default Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(6), pages 1517-1547, December.
    9. Pierre Bajgrowicz & Olivier Scaillet & Adrien Treccani, 2016. "Jumps in High-Frequency Data: Spurious Detections, Dynamics, and News," Management Science, INFORMS, vol. 62(8), pages 2198-2217, August.
    10. Xiaofei Zhao, 2017. "Does Information Intensity Matter for Stock Returns? Evidence from Form 8-K Filings," Management Science, INFORMS, vol. 63(5), pages 1382-1404, May.
    11. repec:taf:jnlbes:v:30:y:2012:i:2:p:242-255 is not listed on IDEAS
    12. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
    13. Martijn Cremers & Michael Halling & David Weinbaum, 2015. "Aggregate Jump and Volatility Risk in the Cross-Section of Stock Returns," Journal of Finance, American Finance Association, vol. 70(2), pages 577-614, April.
    14. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
    15. Brogaard, Jonathan & Carrion, Allen & Moyaert, Thibaut & Riordan, Ryan & Shkilko, Andriy & Sokolov, Konstantin, 2018. "High frequency trading and extreme price movements," Journal of Financial Economics, Elsevier, vol. 128(2), pages 253-265.
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    Cited by:

    1. Markus Bibinger & Nikolaus Hautsch & Alexander Ristig, 2024. "Jump detection in high-frequency order prices," Papers 2403.00819, arXiv.org.

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    More about this item

    Keywords

    Extreme-value theory; Gumbel law; Folded normal distribution; Jump detection;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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