Parameter Estimation of Ornstein-Uhlenbeck Process Using Resampling Estimation Techniques: A Simulation Study

Accurate parameter estimation is essential in diverse fields such as finance, ecology, and physics, where stochastic processes form a fundamental component. This study aims to compare resampling estimation methods including, bootstrap, jackknife, and jackknife-after-bootstrap for parameter estimation in the Ornstein-Uhlenbeck (OU) process. The findings from the results indicated that the bootstrap method outperforms the other resampling methods with respect to bias estimation and standard error. Consequently, the bootstrap method provided more precise standard error estimates (average of 0.08) compared to jackknife (0.12) and jackknife-after-bootstrap (0.11). The Jarque-Bera test as well as Q-Q plot of normality confirmed that applying the bootstrap method to estimate the OU parameters of the model is adequate. It is, therefore, recommended to implement the bootstrap resampling method on real-life data (preferably lending rate) to demonstrate its behavior in estimating mean-reverting parameters and also serve as validation for the efficacy of our methodology.