Open Access
2022 Noise inference for ergodic Lévy driven SDE
Hiroki Masuda, Lorenzo Mercuri, Yuma Uehara
Author Affiliations +
Electron. J. Statist. 16(1): 2432-2474 (2022). DOI: 10.1214/22-EJS2006


We study inference for the driving Lévy noise of an ergodic stochastic differential equation (SDE) model, when the process is observed at high-frequency and long time and when the drift and scale coefficients contain finite-dimensional unknown parameters. By making use of the Gaussian quasi-likelihood function for the coefficients, we derive a stochastic expansion for functionals of the unit-time residuals, which clarifies some quantitative effect of plugging in the estimators of the coefficients, thereby enabling us to take several inference procedures for the driving-noise characteristics into account. We also present new classes and methods available in YUIMA for the simulation and the estimation of a Lévy SDE model. We highlight the flexibility of these new advances in YUIMA using simulated and real data.

Funding Statement

This work was partly supported by JST CREST Grant Number JPMJCR14D7, Japan.


We thank the anonymous reviewers for their valuable comments. This work was partly supported by JST CREST Grant Number JPMJCR14D7, Japan.


Download Citation

Hiroki Masuda. Lorenzo Mercuri. Yuma Uehara. "Noise inference for ergodic Lévy driven SDE." Electron. J. Statist. 16 (1) 2432 - 2474, 2022.


Received: 1 November 2021; Published: 2022
First available in Project Euclid: 4 April 2022

Digital Object Identifier: 10.1214/22-EJS2006

Primary: 62F12 , 62M20
Secondary: 60G51 , 62-04

Keywords: Gaussian quasi-likelihood function , Noise Inference , SDE driven by a Lévy process

Vol.16 • No. 1 • 2022
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