  We study inference for the driving L\'evy 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 L\'evy SDE model. We
highlight the flexibility of these new advances in YUIMA using simulated and
real data.
