Change-point Estimation of a Mean Shift in Moving-average Processes Under Dependence Assumptions

Abstract

In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρ-mixing, φ-mixing, α-mixing sequences under suitable conditions. These results extend those of Bai [1], who studied the mean shift point of a linear process of i.i.d. variables, and the condition $$ {\sum\limits_{j = 0}^\infty {j{\left| {a_{j} } \right|}} } < \infty $$ in Bai is weakened to $$ {\sum\limits_{j = 0}^\infty {{\left| {a_{j} } \right|}} } < \infty $$ .