Small sample properties of ML estimator in Vasicek and CIR models: a simulation experiment

In this paper we analyze small sample properties of the ML estimation procedure in Vasicek and CIR models. In particular, we consider short time series, with a length between 20 and 200, typically values observed in the field of survival data. We perform a simulation study in order to investigate which properties of the parameter estimators still remain valid and to evaluate the effect of a bootstrap bias correction method. The results show that the bias of the estimators can be really strong for small samples and the relative bias seems to be worse when the true parameters of the models are near to the nonstationarity case. The bootstrap bias correction is enough efficient in correcting the bias also for very small sample sizes, but the increase in RMSE of the estimator is greater as much as smaller is the bias in the ML estimator. Moreover, the bootstrap correction does not improve the performance of the tests on the parameters.