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.

Noise inference for ergodic Lévy driven SDE / H. Masuda, L. Mercuri, Y. Uehara. - In: ELECTRONIC JOURNAL OF STATISTICS. - ISSN 1935-7524. - 16:1(2022 Apr), pp. 2432-2474. [10.1214/22-EJS2006]

Noise inference for ergodic Lévy driven SDE

L. Mercuri
Penultimo
;
2022

Abstract

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.
Noise Inference; Lévy process; SDE estimation;
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
apr-2022
https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-16/issue-1/Noise-inference-for-ergodic-Lévy-driven-SDE/10.1214/22-EJS2006.full
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/917170
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