Estimating the degree of activity of jumps in high frequency data

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Abstract

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
Volume37
Issue number5 A
DOIs
StatePublished - Oct 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

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

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