Optimal stable Ornstein-Uhlenbeck regression

TL;DR

This paper develops efficient inference methods for an Ornstein-Uhlenbeck regression model driven by a non-Gaussian stable Levy process, focusing on high-frequency data and asymptotic properties.

Contribution

It introduces local asymptotics for the likelihood and constructs an asymptotically efficient estimator using a simple preliminary approach.

Findings

Derived local asymptotics for the likelihood function

Constructed an asymptotically efficient estimator

Applicable to high-frequency observations of non-Gaussian processes

Abstract

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.