This paper considers the problem of testing for the presence of a continuous part in a semimartingale sampled at high frequency. We provide two tests, one where the null hypothesis is that a continuous component is present, the other where the continuous component is absent, and the model is then driven by a pure jump process. When applied to high-frequency individual stock data, both tests point toward the need to include a continuous component in the model.
@article{1284391759,
author = {A\"\i t-Sahalia, Yacine and Jacod, Jean},
title = {Is Brownian motion necessary to model high-frequency data?},
journal = {Ann. Statist.},
volume = {38},
number = {1},
year = {2010},
pages = { 3093-3128},
language = {en},
url = {http://dml.mathdoc.fr/item/1284391759}
}
Aït-Sahalia, Yacine; Jacod, Jean. Is Brownian motion necessary to model high-frequency data?. Ann. Statist., Tome 38 (2010) no. 1, pp. 3093-3128. http://gdmltest.u-ga.fr/item/1284391759/