We study the bias and the mean-squared error of the maximum likelihood estimators (MLE) of parameters associated with a two-parameter mean-reverting process for a finite time $T$. Using the likelihood ratio process, we derive the expressions for MLEs, then compute the bias and the MSE via the change of measure and Ito's formula. We apply the derived expressions to the general Ornstein-Uhlenbeck process, where the bias and the MSE are numerically computed through a joint moment-generating function of key functionals of the O-U process. A numerical study is provided to illustrate the behaviour of bias and the MSE for the MLE of the mean-reverting speed parameter.

翻译：本文研究了与双参数均值回归过程相关的最大似然估计量（MLE）在有限时间$T$内的偏差和均方误差。利用似然比过程，我们推导了MLE的表达式，随后通过测度变换和伊藤公式计算了偏差和均方误差。我们将推导出的表达式应用于一般奥恩斯坦-乌伦贝克过程，其中偏差和均方误差通过该过程关键泛函的联合矩母函数进行数值计算。数值研究展示了均值回归速度参数MLE的偏差和均方误差的行为特征。