Asymptotic theory for explosive fractional Ornstein-Uhlenbeck processes

Abstract

This paper proposes estimators for the parameters of an explosive fractional Ornstein-Uhlenbeck process. The asymptotic properties for the diffusion estimators are developed under the in-fill asymptotic scheme, while the asymptotic properties for the drift estimators are developed under the double asymptotic scheme for the full range of the Hurst parameter. The double asymptotic distribution of the estimator of the persistency parameter explicitly depends on the initial condition. Simulation results demonstrate the effectiveness of the proposed estimators, and the asymptotic distributions provide a good approximation in finite samples. An empirical application is presented to demonstrate the model’s usefulness and the practical value of the asymptotic theory.