Limit theorems for power variations of pure-jump processes with application to activity estimation
Probability
2011-04-07 v1
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
Cite
@article{arxiv.1104.1064,
title = {Limit theorems for power variations of pure-jump processes with application to activity estimation},
author = {Viktor Todorov and George Tauchen},
journal= {arXiv preprint arXiv:1104.1064},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AAP700 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)