Robust CUSUM-M test in the presence of long-memory disturbances

Abstract

We derive the limiting null distribution of the robust CUSUM-M test and the recursive CUSUM-M test for structural change of the coefficients of a linear regression model with long-memory disturbances. It turns out that the asymptotic null distribution of the CUSUM-M statistic is a fractional Brownian Bridge and the asymptotic null distribution of the recursive CUSUM-M statistic is fractional Brownian motion.