Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function

Résumé

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 at the instants (t n i)i=0,...,n with ∆n = sup i=0,...,n−1 (t n i+1 − t n i) → 0. 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 ∆n → 0, assuming a finite jump activity. This extends earlier results where a condition on the step discretization was needed (see [13],[28]) 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∆ k n → 0 where k > 0 can be arbitrarily large. This extends the results obtained by Kessler [17] in the case of continuous processes. Efficient drift estimation, efficient volatility estimation,ergodic properties, high frequency data, Lévy-driven SDE, thresholding methods.
Fichier principal
Vignette du fichier
Joint_estimation_for_volatility_and_drift_parameters_of_ergodic_jump_diffusion_processes_via_contrast_function.pdf (716.43 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02331156 , version 1 (24-10-2019)
hal-02331156 , version 2 (24-11-2020)

Identifiants

Citer

Chiara Amorino, Arnaud Gloter. Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function. 2020. ⟨hal-02331156v2⟩
90 Consultations
86 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More