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.
Publié le : 2011-04-15
Classification:
Activity index,
Blumenthal–Getoor index,
central limit theorem,
Itô semimartingale,
high-frequency data,
jumps,
realized power variation,
62F12,
62M05,
60H10,
60J60
@article{1300800981,
author = {Todorov, Viktor and Tauchen, George},
title = {Limit theorems for power variations of pure-jump processes with application to activity estimation},
journal = {Ann. Appl. Probab.},
volume = {21},
number = {1},
year = {2011},
pages = { 546-588},
language = {en},
url = {http://dml.mathdoc.fr/item/1300800981}
}
Todorov, Viktor; Tauchen, George. Limit theorems for power variations of pure-jump processes with application to activity estimation. Ann. Appl. Probab., Tome 21 (2011) no. 1, pp. 546-588. http://gdmltest.u-ga.fr/item/1300800981/