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

36 Pages Posted: 6 Oct 2010

Date Written: March 18, 2010

Abstract

This paper derives the asymptotic behavior of realized power variation of pure-jump Ito 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 Ito semimartingale over a fixed interval.

Keywords: Activity Index, Blumenthal-Getoor Index, Central Limit Theorem, Ito Semimartingale, High-Frequency Data, Jumps, Realized Power Variation

Suggested Citation

Todorov, Viktor and Tauchen, George E., Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation (March 18, 2010). Economic Research Initiatives at Duke (ERID) Working Paper No. 74, Available at SSRN: https://ssrn.com/abstract=1687968 or http://dx.doi.org/10.2139/ssrn.1687968

Viktor Todorov (Contact Author)

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

George E. Tauchen

Duke University - Economics Group ( email )

Box 90097
221 Social Sciences
Durham, NC 27708-0097
United States
919-660-1812 (Phone)
919-684-8974 (Fax)

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