Open Access
April 2012 Realized Laplace transforms for pure-jump semimartingales
Viktor Todorov, George Tauchen
Ann. Statist. 40(2): 1233-1262 (April 2012). DOI: 10.1214/12-AOS1006


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.


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Viktor Todorov. George Tauchen. "Realized Laplace transforms for pure-jump semimartingales." Ann. Statist. 40 (2) 1233 - 1262, April 2012.


Published: April 2012
First available in Project Euclid: 18 July 2012

zbMATH: 1274.62191
MathSciNet: MR2985949
Digital Object Identifier: 10.1214/12-AOS1006

Primary: 62F12 , 62M05
Secondary: 60H10 , 60J75

Keywords: high-frequency data , inference , jumps , Laplace transform , time-varying scale

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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