Open Access
October 2010 Is Brownian motion necessary to model high-frequency data?
Yacine Aït-Sahalia, Jean Jacod
Ann. Statist. 38(5): 3093-3128 (October 2010). DOI: 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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Yacine Aït-Sahalia. Jean Jacod. "Is Brownian motion necessary to model high-frequency data?." Ann. Statist. 38 (5) 3093 - 3128, October 2010.


Published: October 2010
First available in Project Euclid: 13 September 2010

zbMATH: 1327.62118
MathSciNet: MR2722465
Digital Object Identifier: 10.1214/09-AOS749

Primary: 62F12 , 62M05
Secondary: 60H10 , 60J60

Keywords: Brownian motion , discrete sampling , finite activity , high frequency , infinite activity , jumps , Semimartingale

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 5 • October 2010
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