Estimating the degree of activity of jumps in high frequency data

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179 Scopus citations


We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the process, which makes it more challenging to infer the characteristics of the small, infinite activity jumps. When the method is applied to high frequency stock returns, we find evidence of infinitely active jumps in the data and estimate their index of activity.

Original languageEnglish (US)
Pages (from-to)2202-2244
Number of pages43
JournalAnnals of Statistics
Issue number5 A
StatePublished - Oct 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Discrete sampling
  • High frequency
  • Index of activity
  • Infinite activity
  • Jumps


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