Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency

11/18/2022

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by   Khalifa Es-Sebaiy, et al.

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This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted θ, for a Ornstein-Uhlenbeck process X {X_t,t≥0} observed at high frequency. We provide an Approximate minimum contrast estimator and an approximate maximum likelihood estimator of θ, namely θ_n1/(2/n∑_i=1^nX_t_i^2), and θ_n -∑_i=1^n X_t_i-1(X_t_i-X_t_i-1)/(Δ_n∑_i=1^n X_t_i-1^2), respectively, where t_i = i Δ_n, i=0,1,…, n, Δ_n→ 0. We provide Wasserstein bounds in central limit theorem for θ_n and θ_n.