Volatility occupation times

Jia Li, Viktor Todorov, George Tauchen

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a kernel-based estimator of its density. We prove the consistency of our estimators and further derive bounds for their rates of convergence. We use these results to estimate nonparametrically the quantiles associated with the volatility occupation measure.

Original languageEnglish (US)
Pages (from-to)1865-1891
Number of pages27
JournalAnnals of Statistics
Volume41
Issue number4
DOIs
StatePublished - Aug 2013

Keywords

  • High-frequency data
  • Local approximation
  • Nonparametric estimation
  • Occupation time
  • Quantiles
  • Spot variance
  • Stochastic volatility

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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