Irregular sampling and central limit theorems for power variations: The continuous case

Takaki Hayashi, Jean Jacod, Nakahiro Yoshida

Research output: Contribution to journalArticle

27 Citations (Scopus)


In the context of high frequency data, one often has to deal with observations occurring at irregularly spaced times, at transaction times for example in finance. Here we examine how the estimation of the squared or other powers of the volatility is affected by irregularly spaced data. The emphasis is on the kind of assumptions on the sampling scheme which allow to provide consistent estimators, together with an associated central limit theorem, and especially when the sampling scheme depends on the observed process itself.

Original languageEnglish
Pages (from-to)1197-1218
Number of pages22
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number4
Publication statusPublished - 2011 Nov 1



  • Discrete observations
  • High frequency data
  • Power variations
  • Quadratic variation
  • Stable convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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