Noise inference for ergodic Lévy driven SDE

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.