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

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

2011-04-06

arxiv.org/abs/1104.1064v1

Annals of Applied Probability 2011, Vol. 21, No. 2, 546-588

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AAP700 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/10-AAP700

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.

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