Is brownian motion necessary to model high-frequency data?

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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.

Original languageEnglish (US)
Pages (from-to)3093-3128
Number of pages36
JournalAnnals of Statistics
Issue number5
StatePublished - Oct 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Brownian motion
  • Discrete sampling
  • Finite activity
  • High frequency.
  • Infinite activity
  • Jumps
  • Semimartingale


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