Statistical analysis of the mixed fractional Ornstein--Uhlenbeck process

TL;DR

This paper investigates the estimation of the drift parameter in a mixed fractional Ornstein-Uhlenbeck process, demonstrating the consistency and asymptotic normality of the maximum likelihood estimator using spectral analysis of mixed processes.

Contribution

It introduces a rigorous analysis of the maximum likelihood estimator for the mixed fractional Ornstein-Uhlenbeck process, leveraging recent spectral results.

Findings

MLE is consistent for the drift parameter

MLE is asymptotically normal in large samples

Spectral methods are effective for mixed processes

Abstract

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