Realized laplace transforms for pure-jump semimartingales

Journal Article

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. © Institute of Mathematical Statistics, 2012.

Full Text

Duke Authors

Cited Authors

  • Todorov, V; Tauchen, G

Published Date

  • 2012

Published In

Volume / Issue

  • 40 / 2

Start / End Page

  • 1233 - 1262

International Standard Serial Number (ISSN)

  • 0090-5364

Digital Object Identifier (DOI)

  • 10.1214/12-AOS1006