Least squares estimator of fractional Ornstein Uhlenbeck processes with periodic mean

TL;DR

This paper investigates the estimation of drift parameters in fractional Ornstein-Uhlenbeck processes with periodic mean, extending previous results to broader Hurst parameter ranges and analyzing asymptotic properties.

Contribution

It extends the strong consistency results for drift estimation in fractional OU processes with periodic mean to all H in (1/2,1) and discusses asymptotic normality.

Findings

Extended strong consistency to all H in (1/2,1)

Analyzed asymptotic normality of the estimators

Studied processes of the second kind with periodic mean

Abstract

We first study the drift parameter estimation of the fractional Ornstein-Uhlenbeck process (fOU) with periodic mean for every $\frac{1}{2}<H<1$. More precisely, we extend the consistency proved in \cite{DFW} for $\frac{1}{2}<H<\frac{3}{4}$ to the strong consistency for any $\frac{1}{2}<H<1$ on the one hand, and on the other, we also discuss the asymptotic normality given in \cite{DFW}. In the second main part of the paper, we study the strong consistency and the asymptotic normality of the fOU of the second kind with periodic mean for any $\frac{1}{2}<H<1$.