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The Gumbel test and jumps in the volatility process

Author

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  • Christian Palmes

    (Technische Universität Dortmund)

  • Jeannette H. C. Woerner

    (Technische Universität Dortmund)

Abstract

In the framework of jump detection in stochastic volatility models the Gumbel test based on extreme value theory has recently been introduced. Compared to other jump tests it possesses the advantages that the direction and location of jumps may also be detected. Furthermore, compared to the Barndorff–Nielsen and Shephard test based on bipower variation the Gumbel test possesses a larger power. However, so far one assumption was that the volatility process is Hölder continuous, though there is empirical evidence for jumps in the volatility as well. In this paper we derive that the Gumbel test still works under the setting of finitely many jumps not exceeding a certain size. This maximal jump size depends on the relative sampling frequencies involved in the definition of the test statistics. Furthermore, we show that the given bound on the jump size is sharp and investigate the details of the phase transition at this critical bound.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:19:y:2016:i:2:d:10.1007_s11203-015-9127-8
    DOI: 10.1007/s11203-015-9127-8
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    2. 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.
    3. 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.
    4. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
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    Cited by:

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    2. 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).

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