A Least Squares Estimator for Gradual Change-Point in Time Series with m-Asymptotically Almost Negatively Associated Errors

Abstract

As a new member of the NA (negative associated) family, the m-AANA (m-asymptotically almost negatively associated) sequence has many statistical properties that have not been developed. This paper mainly studies its properties in the gradual change point model. Firstly, we propose a least squares type change point estimator, then derive the convergence rates and consistency of the estimator, and provide the limit distributions of the estimator. It is interesting that the convergence rates of the estimator are the same as that of the change point estimator for independent identically distributed observations. Finally, the effectiveness of the estimator in limited samples can be verified through several sets of simulation experiments and an actual hydrological example.