Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation

Viktor Todorov and George Tauchen ()

No 10-74, Working Papers from Duke University, Department of Economics

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 e±cient adaptive estimator for the activity of discretely-sampled It^o semimartingale over a fixed interval.

Keywords: Activity index; Blumenthal-Getoor index; Central Limit Theorem; It^o semimartingale; high-frequency data; jumps; realized power variation (search for similar items in EconPapers)
Pages: 35
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:duk:dukeec:10-74

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