Asymptotic properties of realized power variations and related functionals of semimartingales
Probability
2007-05-23 v1
Abstract
This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is 2 we get the realized quadratic variation) . We prove a variety of ``laws of large numbers'', that is convergence in probability of these sums, sometimes after normalization. We also exhibit in many cases the rate of convergence, as well as associated central limit theorems.
Keywords
Cite
@article{arxiv.math/0604450,
title = {Asymptotic properties of realized power variations and related functionals of semimartingales},
author = {Jean Jacod},
journal= {arXiv preprint arXiv:math/0604450},
year = {2007}
}