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

Viktor Todorov; George Tauchen

doi:10.1214/10-AAP700

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

Viktor Todorov^*, George Tauchen

^*Corresponding author for this work

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26 Scopus citations

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.

Original language	English (US)
Pages (from-to)	546-588
Number of pages	43
Journal	Annals of Applied Probability
Volume	21
Issue number	2
DOIs	https://doi.org/10.1214/10-AAP700
State	Published - Apr 1 2011

Keywords

Activity index
Blumenthal-Getoor index
Central limit theorem
High-frequency data
Itô semimartingale
Jumps
Realized power variation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/10-AAP700

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abstract = "This paper derives the asymptotic behavior of realized power variation of pure-jump It{\^o} 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 It{\^o} semimartingale over a fixed interval.",

keywords = "Activity index, Blumenthal-Getoor index, Central limit theorem, High-frequency data, It{\^o} semimartingale, Jumps, Realized power variation",

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AU - Tauchen, George

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AB - 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.

KW - Activity index

KW - Blumenthal-Getoor index

KW - Central limit theorem

KW - High-frequency data

KW - Itô semimartingale

KW - Jumps

KW - Realized power variation

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

Abstract

Keywords

ASJC Scopus subject areas

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