Asymptotic inference for reflected Brownian motions

Abstract

In this work, estimation and testing methods for Brownian motions in the presence of two reflecting barriers are analysed. By deriving the autocovariance function of the reflected Brownian motion, the asymptotic distributions of ordinary least squares esti-mators and Dickey-Fuller test statistics are obtained and the presence of inconsistency problems is evaluated analytically. A special attention is paid to the problem of testing for reflected Brownian motion dynamics in the presence of a non-zero drift and a test, which is based on the sample first-order autoregressive coefficient, is proposed.