- Volume 17, Number 2 (2011), 781-813.
Nonparametric tests for pathwise properties of semimartingales
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.
Bernoulli, Volume 17, Number 2 (2011), 781-813.
First available in Project Euclid: 5 April 2011
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Cont, Rama; Mancini, Cecilia. Nonparametric tests for pathwise properties of semimartingales. Bernoulli 17 (2011), no. 2, 781--813. doi:10.3150/10-BEJ293. https://projecteuclid.org/euclid.bj/1302009247