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Nonparametric tests for pathwise properties of semimartingales

Author

Listed:
  • 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)

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.

Suggested Citation

  • Rama Cont & Cecilia Mancini, 2010. "Nonparametric tests for pathwise properties of semimartingales," Working Papers - Mathematical Economics 2010-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    • Handle: RePEc:flo:wpaper:2010-02
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    References listed on IDEAS

    as
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    5. Mancini, Cecilia & Renò, Roberto, 2011. "Threshold estimation of Markov models with jumps and interest rate modeling," Journal of Econometrics, Elsevier, vol. 160(1), pages 77-92, January.
    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, June.
    7. 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.
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    Cited by:

    1. Cecilia Mancini, 2010. "Speed of convergence of the threshold estimator of integrated variance," Working Papers - Mathematical Economics 2010-03, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

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    More about this item

    Keywords

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