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Volatility occupation times

Publication ,  Journal Article
Li, J; Todorov, V; Tauchen, G
Published in: Annals of Statistics
2013

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. © Institute of Mathematical Statistics, 2013.

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Published In

Annals of Statistics

DOI

ISSN

0090-5364

Publication Date

2013

Volume

41

Issue

4

Start / End Page

1865 / 1891

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Li, J., Todorov, V., & Tauchen, G. (2013). Volatility occupation times. Annals of Statistics, 41(4), 1865–1891. https://doi.org/10.1214/13-AOS1135
Li, J., V. Todorov, and G. Tauchen. “Volatility occupation times.” Annals of Statistics 41, no. 4 (2013): 1865–91. https://doi.org/10.1214/13-AOS1135.
Li J, Todorov V, Tauchen G. Volatility occupation times. Annals of Statistics. 2013;41(4):1865–91.
Li, J., et al. “Volatility occupation times.” Annals of Statistics, vol. 41, no. 4, 2013, pp. 1865–91. Scival, doi:10.1214/13-AOS1135.
Li J, Todorov V, Tauchen G. Volatility occupation times. Annals of Statistics. 2013;41(4):1865–1891.

Published In

Annals of Statistics

DOI

ISSN

0090-5364

Publication Date

2013

Volume

41

Issue

4

Start / End Page

1865 / 1891

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics