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Parameter estimation for the drift of a time inhomogeneous jump diffusion process
Author(s) -
Franke Brice,
Kott Thomas
Publication year - 2013
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2012.00537.x
Subject(s) - jump , estimator , jump diffusion , mathematics , consistency (knowledge bases) , jump process , diffusion , asymptotic distribution , diffusion process , estimation theory , term (time) , statistical physics , statistics , computer science , physics , knowledge management , geometry , innovation diffusion , quantum mechanics , thermodynamics
This work deals with parameter estimation for the drift of jump diffusion processes which are driven by a Lévy process and whose drift term is linear in the parameter. In contrast to the commonly used maximum likelihood estimator, our proposed estimator has the practical advantage that its calculation does not require the evaluation of the continuous part of the sample path. In the important case of an Ornstein‐Uhlenbeck‐type jump diffusion, which is a widely used model, we prove consistency and asymptotic normality.