Limit theorems for power variations of pure-jump processes with application to activity estimation

Viktor Todorov*, George Tauchen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

This paper derives the asymptotic behavior of realized power variation of pure-jump Itô semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a function of its power. We apply the limit theorems to propose an efficient adaptive estimator for the activity of discretely-sampled Itô semimartingale over a fixed interval.

Original languageEnglish (US)
Pages (from-to)546-588
Number of pages43
JournalAnnals of Applied Probability
Volume21
Issue number2
DOIs
StatePublished - Apr 1 2011

Keywords

  • Activity index
  • Blumenthal-Getoor index
  • Central limit theorem
  • High-frequency data
  • Itô semimartingale
  • Jumps
  • Realized power variation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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