Volatility estimators for discretely sampled Lévy processes

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Abstract

This paper studies the estimation of the volatility parameter in a model where the driving process is a Brownian motion or a more general symmetric stable process that is perturbed by another Lévy process. We distinguish between a parametric case, where the law of the perturbing process is known, and a semiparametric case, where it is not. In the parametric case, we construct estimators which are asymptotically efficient. In the semiparametric case, we can obtain asymptotically efficient estimators by sampling at a sufficiently high frequency, and these estimators are efficient uniformly in the law of the perturbing process.

Original languageEnglish (US)
Pages (from-to)355-392
Number of pages38
JournalAnnals of Statistics
Volume35
Issue number1
DOIs
StatePublished - Feb 1 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Discrete sampling
  • Efficiency
  • Inference
  • Jumps

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