Reference : Contrast function estimation for the drift parameter of ergodic jump diffusion process
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Contrast function estimation for the drift parameter of ergodic jump diffusion process
Amorino, Chiara* mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Gloter, Arnaud* [Université d'Evry > LaMMe]
* These authors have contributed equally to this work.
Scandinavian Journal of Statistics
Yes (verified by ORBilu)
United Kingdom
[en] Efficient drift estimation ; ergodic properties ; high frequency ; Levy processes ; thresholding methods ; SDE with jumps
[en] In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter. We suppose that the process is discretely observed. We introduce an estimator based on a contrast function, which is efficient without requiring any conditions on the rate at which the step discretization goes to zero, and where we allow the observed process to have non summable jumps. This extends earlier results where the condition on the step discretization was needed and where the process was supposed to have summable jumps. In general situations, our contrast function is not explicit and one has to resort to some approximation. In the case of a finite jump activity, we propose explicit approximations of the contrast function, such that the efficient estimation of the drift parameter is feasible. This extends the results obtained by Kessler in the case of continuous processes.

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