Nadaraya-Watson estimator for reflected stochastic processes driven by Brownian motions

TL;DR

This paper develops and analyzes Nadaraya-Watson estimators for the drift function of reflected stochastic processes, providing consistency, asymptotic distributions, and practical numerical validation.

Contribution

It introduces both discrete and continuous N-W estimators for reflected processes and establishes their theoretical properties, extending their applicability.

Findings

Establishes consistency of the estimators

Derives asymptotic distributions for the estimators

Numerical studies confirm practical effectiveness

Abstract

We study the Nadaraya-Watson (N-W) estimator for the drift function of two-sided reflected stochastic processes. We propose a discrete-type N-W estimator and a continuous-type N-W estimator based on the discretely observed processes and continuously observed processes respectively. Under some regular conditions, we obtain the consistency and give the asymptotic distributions for the two estimators. Furthermore, we briefly remark that our method can be applied to the one-sided reflected stochastic processes spontaneously. Numerical studies show that the proposed estimators is adequate for practical use.