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.
Publié le : 2011-05-15
Classification:
high frequency data,
jump processes,
nonparametric tests,
quadratic variation,
realized volatility,
semimartingale
@article{1302009247,
author = {Cont, Rama and Mancini, Cecilia},
title = {Nonparametric tests for pathwise properties of semimartingales},
journal = {Bernoulli},
volume = {17},
number = {1},
year = {2011},
pages = { 781-813},
language = {en},
url = {http://dml.mathdoc.fr/item/1302009247}
}
Cont, Rama; Mancini, Cecilia. Nonparametric tests for pathwise properties of semimartingales. Bernoulli, Tome 17 (2011) no. 1, pp. 781-813. http://gdmltest.u-ga.fr/item/1302009247/