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

First available in Project Euclid: 22 March 2011

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Zentralblatt MATH identifier

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]

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


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.

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