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Limit theorems for power variations of pure-jump processes with application to activity estimation

Publication ,  Journal Article
Todorov, V; Tauchen, G
Published in: Annals of Applied Probability
2011

This paper derives the asymptotic behavior of realized power variation of pure-jump Itô semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a function of its power. We apply the limit theorems to propose an efficient adaptive estimator for the activity of discretely-sampled Itô semimartingale over a fixed interval. © Institute of Mathematical Statistics, 2011.

Duke Scholars

Published In

Annals of Applied Probability

DOI

ISSN

1050-5164

Publication Date

2011

Volume

21

Issue

2

Start / End Page

546 / 588

Related Subject Headings

  • Statistics & Probability
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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MLA
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Todorov, V., & Tauchen, G. (2011). Limit theorems for power variations of pure-jump processes with application to activity estimation. Annals of Applied Probability, 21(2), 546–588. https://doi.org/10.1214/10-AAP700
Todorov, V., and G. Tauchen. “Limit theorems for power variations of pure-jump processes with application to activity estimation.” Annals of Applied Probability 21, no. 2 (2011): 546–88. https://doi.org/10.1214/10-AAP700.
Todorov V, Tauchen G. Limit theorems for power variations of pure-jump processes with application to activity estimation. Annals of Applied Probability. 2011;21(2):546–88.
Todorov, V., and G. Tauchen. “Limit theorems for power variations of pure-jump processes with application to activity estimation.” Annals of Applied Probability, vol. 21, no. 2, 2011, pp. 546–88. Scival, doi:10.1214/10-AAP700.
Todorov V, Tauchen G. Limit theorems for power variations of pure-jump processes with application to activity estimation. Annals of Applied Probability. 2011;21(2):546–588.

Published In

Annals of Applied Probability

DOI

ISSN

1050-5164

Publication Date

2011

Volume

21

Issue

2

Start / End Page

546 / 588

Related Subject Headings

  • Statistics & Probability
  • 0104 Statistics
  • 0102 Applied Mathematics