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Nonparametric tests for pathwise properties of semimartingales


  • 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)


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

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    More about this item


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

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