Asymptotic expansion of the drift estimator for the fractional Ornstein-Uhlenbeck process

2024/03/01 by Ciprian A. Tudor, Tudor, Ciprian A., Nakahiro Yoshida +1
Economics, Econometrics and Finance · Mathematics · #60F05 #62H12 #62M09 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2403.00967

openalex publication_date 2024/03/01 · openalex created_date 2024/03/06 · openalex updated_date 2026/07/28

Abstract

We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the authors [26]. The central limit theorem in the principal part of the expansion has the classical scaling T^1/2. However, the asymptotic expansion formula is a complex in that the order of the correction term becomes the classical T^-1/2 for H in (1/2,5/8), but T^4H-3 for H in [5/8, 3/4).

Related

• A Note On Inference for the Mixed Fractional Ornstein-Uhlenbeck Process with Drift
• Estimating Drift Parameters in a Fractional Ornstein Uhlenbeck Process with Periodic Mean
• Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the Second Kind
• Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter
• Berry-Esséen bound for drift estimation of fractional Ornstein Uhlenbeck process of second kind