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Nonparametric tests for pathwise properties of semimartingales

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Author Info

  • Rama Cont

    ()
    (IEOR Dept., Columbia University, New York, USA, and Laboratoire de Probabilites et Modeles Aleatoires, CNRS-Universite Paris VI, France)

  • Cecilia Mancini

    ()
    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

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    Abstract

    We propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a L\'evy process and a Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the quadratic variation, we design a test for the presence of a continuous martingale component in the process and a test for establishing whether the jumps have finite or infinite variation, based on observations on a discrete time grid. We evaluate the performance of our tests using simulations of various stochastic models and use the tests to investigate the fine structure of the DM/USD exchange rate fluctuations and SPX futures prices. In both cases, our tests reveal the presence of a non-zero Brownian component and a finite variation jump component.

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    File URL: http://www.disei.unifi.it/upload/sub/pubblicazioni/repec/flo/workingpapers/storicodimad/2010n/dimadwp2010-02.pdf
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    Bibliographic Info

    Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2010-02.

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    Length: 22 pages
    Date of creation: Jan 2010
    Date of revision:
    Handle: RePEc:flo:wpaper:2010-02

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    Related research

    Keywords: Threshold estimator; central limit theorem; test for finite variation jumps; test for Brownian component.;

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    1. Peter Carr & Liuren Wu, 2002. "What Type of Process Underlies Options? A Simple Robust Test," Finance 0207019, EconWPA.
    2. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    4. Mancini, Cecilia & RenĂ², Roberto, 2011. "Threshold estimation of Markov models with jumps and interest rate modeling," Journal of Econometrics, Elsevier, vol. 160(1), pages 77-92, January.
    5. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
    6. Cecilia Mancini, 2009. "Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296.
    7. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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