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April 2011 Limit theorems for power variations of pure-jump processes with application to activity estimation
Viktor Todorov, George Tauchen
Ann. Appl. Probab. 21(2): 546-588 (April 2011). DOI: 10.1214/10-AAP700

Abstract

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.

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Viktor Todorov. George Tauchen. "Limit theorems for power variations of pure-jump processes with application to activity estimation." Ann. Appl. Probab. 21 (2) 546 - 588, April 2011. https://doi.org/10.1214/10-AAP700

Information

Published: April 2011
First available in Project Euclid: 22 March 2011

zbMATH: 1215.62088
MathSciNet: MR2807966
Digital Object Identifier: 10.1214/10-AAP700

Subjects:
Primary: 62F12 , 62M05
Secondary: 60H10 , 60J60

Keywords: Activity index , Blumenthal–Getoor index , central limit theorem , high-frequency data , Itô semimartingale , jumps , realized power variation

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 2 • April 2011
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