Nadaraya-Watson estimators for reflected stochastic processes

Abstract

We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations. The estimates, based on either the continuously observed process or the discretely observed process, are considered. Under certain conditions, we prove the strong consistency and the asymptotic normality of the two estimators. Our method is also suitable for one-sided reflected stochastic differential equations. Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al. (Stat Sin, 2021, 31: 29–51). Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.