Realized laplace transforms for pure-jump semimartingales

Viktor Todorov*, George Tauchen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable Lévy densities in the setting where both the time span of the data set increases, and the mesh of the observation grid decreases. The estimation is based on constructing a nonparametric estimate for the empirical Laplace transform of the stochastic scale over a given interval of time by aggregating high-frequency increments of the observed process on that time interval into a statistic we call realized Laplace transform. The realized Laplace transform depends on the activity of the driving pure-jump martingale, and we consider both cases when the latter is known or has to be inferred from the data.

Original languageEnglish (US)
Pages (from-to)1233-1262
Number of pages30
JournalAnnals of Statistics
Volume40
Issue number2
DOIs
StatePublished - Apr 2012

Keywords

  • High-frequency data
  • Inference
  • Jumps
  • Laplace transform
  • Time-varying scale

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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