Realized Laplace transforms for pure-jump semimartingales
Abstract
We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable L\'{e}vy densities in the setting where both the time span of the data set increases, and the mesh of the observation grid decreases. The estimation is based on constructing a nonparametric estimate for the empirical Laplace transform of the stochastic scale over a given interval of time by aggregating high-frequency increments of the observed process on that time interval into a statistic we call realized Laplace transform. The realized Laplace transform depends on the activity of the driving pure-jump martingale, and we consider both cases when the latter is known or has to be inferred from the data.
Cite
@article{arxiv.1207.5615,
title = {Realized Laplace transforms for pure-jump semimartingales},
author = {Viktor Todorov and George Tauchen},
journal= {arXiv preprint arXiv:1207.5615},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOS1006 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)