The Annals of Applied Probability

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

Viktor Todorov and George Tauchen

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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.

Article information

Source
Ann. Appl. Probab., Volume 21, Number 2 (2011), 546-588.

Dates
First available in Project Euclid: 22 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1300800981

Digital Object Identifier
doi:10.1214/10-AAP700

Mathematical Reviews number (MathSciNet)
MR2807966

Zentralblatt MATH identifier
1215.62088

Subjects
Primary: 62F12: Asymptotic properties of estimators 62M05: Markov processes: estimation
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60: Diffusion processes [See also 58J65]

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

Citation

Todorov, Viktor; Tauchen, George. Limit theorems for power variations of pure-jump processes with application to activity estimation. Ann. Appl. Probab. 21 (2011), no. 2, 546--588. doi:10.1214/10-AAP700. https://projecteuclid.org/euclid.aoap/1300800981


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