Nonparametric tests for the pathwise properties of semimartingales

Abstract : We propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a Lévy 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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Article dans une revue
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2011, 17 (2), pp.781-813. <10.3150/10-BEJ293>
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Contributeur : Rama Cont <>
Soumis le : dimanche 24 avril 2011 - 02:45:45
Dernière modification le : lundi 29 mai 2017 - 14:23:02

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Rama Cont, Cecilia Mancini. Nonparametric tests for the pathwise properties of semimartingales. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2011, 17 (2), pp.781-813. <10.3150/10-BEJ293>. <hal-00588490>

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