Reference : Joint estimation for volatility and drift parameters of ergodic jump diffusion proces...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/44781
Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function
English
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.
2020
Statistical Inference for Stochastic Processes
Kluwer Academic Publishers
Yes (verified by ORBilu)
International
1387-0874
1572-9311
Netherlands
[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.
http://hdl.handle.net/10993/44781

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
Joint_estimation_for_volatility_and_drift_parameters_of_ergodic_jump_diffusion_processes_via_contrast_function.pdfAuthor postprint716.43 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.