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

Abstract

This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted $\theta$, for a Ornstein-Uhlenbeck process $X:=\{X_t,t\ge 0\}$ observed at high frequency. We provide an Approximate minimum contrast estimator and an approximate maximum likelihood estimator of $\theta$, namely ${\tilde{\theta }}_n:=1/\left(\frac{2}{n}{\sum }_{i=1}^n{X}_{t_i}^2\right)$, and ${\hat{\theta }}_n:=-{\sum }_{i=1}^n{X}_{t_{i-1}}\left(X_{t_i}-X_{t_{i-1}}\right)/\left({\Delta }_n{\sum }_{i=1}^n{X}_{t_{i-1}}^2\right)$, respectively, where $t_i=i{\Delta }_n$, $i=0,1,\dots ,n$, ${\Delta }_n\to 0$. We provide Wasserstein bounds in central limit theorem for ${\tilde{\theta }}_n$ and ${\hat{\theta }}_n$.

arXiv admin note: text overlap with arXiv:2102.04810