Optimal stable Ornstein-Uhlenbeck regression

We prove some efficient inference results concerning estimation of a Ornstein-Uhlenbeck regression model, which is driven by a non-Gaussian stable Levy process and where the output process is observed at high-frequency over a fixed time period. Local asymptotics for the likelihood function is presented, followed by a way to construct an asymptotically efficient estimator through a suboptimal yet very simple preliminary estimator, which enables us to bypass not only numerical optimization of the likelihood function, but also the multiple-root problem.