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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.
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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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