Nonparametric tests for pathwise properties of semimartingales

Rama Cont () and Cecilia Mancini ()
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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

No 2010-02, Working Papers - Mathematical Economics from Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa

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.

Keywords: Threshold estimator; central limit theorem; test for finite variation jumps; test for Brownian component. (search for similar items in EconPapers)
Pages: 22 pages
Date: 2010-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (1)

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