Statistical Analysis of the Mixed Fractional Ornstein--Uhlenbeck Process

Abstract

This paper addresses the problem of estimating the drift parameter of the Ornstein--Uhlenbeck-type process driven by the sum of independent standard and fractional Brownian motions. With the help of some recent results on the canonical representation and spectral structure of mixed processes, the maximum likelihood estimator is shown to be consistent and asymptotically normal in the large-sample limit.