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Aït-Sahalia, Yacine; Jacod, Jean

Is Brownian motion necessary to model high-frequency data? (English) Zbl 1327.62118

Ann. Stat. 38, No. 5, 3093-3128 (2010).
Summary: 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.

Cited in 1 Review
Cited in 42 Documents

MSC:

62F12 Asymptotic properties of parametric estimators
62M05 Markov processes: estimation; hidden Markov models
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes

Keywords:

semimartingale; Brownian motion; jumps; finite activity; infinite activity; discrete sampling; high frequency
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\textit{Y. Aït-Sahalia} and \textit{J. Jacod}, Ann. Stat. 38, No. 5, 3093--3128 (2010; Zbl 1327.62118)
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References:

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