Nonparametric tests for pathwise properties of semimartingales

Details Nonparametric tests for pathwise properties of semimartingales Nonparametric tests for pathwise properties of semimartingales

2011-04-22

arxiv.org/abs/1104.4429v1

Bernoulli 2011, Vol. 17, No. 2, 781-813

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ293 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ293

We propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a L\'{e}vy 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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