Contrast function estimation for the drift parameter of ergodic jump diffusion process

Abstract : In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter θ. 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, based on a contrast function, which is efficient without requiring any conditions on the rate at which ∆n → 0, and where we allow the observed process to have non summable jumps. This extends earlier results where the condition n∆ 3 n → 0 was needed (see [10],[24]) and where the process was supposed to have summable jumps. Moreover, in the case of a finite jump activity, we propose explicit approximations of the contrast function, such that the efficient 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 [15] in the case of continuous processes. Lévy-driven SDE, efficient drift estimation, high frequency data, ergodic properties, thresholding methods.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [28 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01842514
Contributor : Arnaud Gloter <>
Submitted on : Tuesday, September 3, 2019 - 4:19:04 PM
Last modification on : Saturday, September 14, 2019 - 1:20:05 AM

Files

contrast_drift_v2.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01842514, version 2
  • ARXIV : 1807.08965

Citation

Chiara Amorino, Arnaud Gloter. Contrast function estimation for the drift parameter of ergodic jump diffusion process. 2019. ⟨hal-01842514v2⟩

Share

Metrics

Record views

14

Files downloads

78