The asymptotic distribution of CUSUM estimator based on α-mixing sequences

Abstract

In this paper, we consider the CUSUM estimator based on α-mixing sequences. By giving the consistency estimators for mean and covariance functions, the limit distribution of CUSUM estimator is presented as a standard Brownian bridge, which can be used in the change point detection. As applications, some simulations and real data examples are illustrated to test our CUSUM estimator.