Is Brownian motion necessary to model high-frequency data?

Details Is Brownian motion necessary to model high-frequency data? Is Brownian motion necessary to model high-frequency data?

2010-11-11

arxiv.org/abs/1011.2635v1

Annals of Statistics 2010, Vol. 38, No. 5, 3093-3128

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS749 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS749

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.

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