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

Journal Article

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. © Institute of Mathematical Statistics, 2011.

Full Text

Duke Authors

Cited Authors

  • Todorov, V; Tauchen, G

Published Date

  • 2011

Published In

Volume / Issue

  • 21 / 2

Start / End Page

  • 546 - 588

International Standard Serial Number (ISSN)

  • 1050-5164

Digital Object Identifier (DOI)

  • 10.1214/10-AAP700