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 Lévy 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.

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)

References in corpus (5)

• Estimating the degree of activity of jumps in high frequency data
• Maximum likelihood estimation for $\alpha$-stable autoregressive processes
• Spectral estimation of the fractional order of a Lévy process
• Statistical inference for time-changed Lévy processes via composite characteristic function estimation
• Limit theorems for power variations of pure-jump processes with application to activity estimation

Cited by in corpus (7)

• Efficient estimation of integrated volatility in presence of infinite variation jumps
• Jump activity estimation for pure-jump semimartingales via self-normalized statistics
• Limit theorems for the empirical distribution function of scaled increments of Itô semimartingales at high frequencies
• Parametric estimation of Lévy processes
• Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process
• Permutation-based tests for discontinuities in event studies
• Large Deviation principles of Realized Laplace Transform of Volatility