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

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.


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
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