Reference : Joint estimation for volatility and drift parameters of ergodic jump diffusion proces...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function
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.
Statistical Inference for Stochastic Processes
Kluwer Academic Publishers
Yes (verified by ORBilu)
[en] Drift estimation ; volatility estimation ; ergodic properties ; high frequency data ; thresholding methods ; SDE with jumps
[en] In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on μ and volatility coefficient depends on σ, two unknown parameters. We suppose that the process is
discretely observed. We introduce an estimator of θ := (μ, σ), based on a contrast function, which is asymptotically gaussian without requiring any conditions on the rate at which the discretisation step goes to 0, assuming a finite jump activity. This extends earlier results where a condition on the step discretization was needed (see [15],[36]) or where only the estimation of the drift parameter was considered (see [2]). In general situations, our contrast function is not explicit and in practise one has to resort to some approximation. We propose explicit approximations of the contrast function, such that the estimation of θ is feasible under the condition that n∆n^k → 0 where k > 0 can be arbitrarily large. This extends the results obtained by Kessler [24] in the case of continuous processes.

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