The Consistency of the CUSUM-Type Estimator of the Change-Point and Its Application

In this paper, we investigate the CUSUM-type estimator of mean change-point models based on m-asymptotically almost negatively associated (m-AANA) sequences. The family of m-AANA sequences contains AANA, NA, m-NA, and independent sequences as special cases. Under some weak conditions, some convergence rates are obtained such as O-P(n(1/p-1)), O-P(n(1/p-1) log(1/p) n) and O-P(n(alpha-1)), where 0 <= alpha < 1 and 1 < p <= 2. Our rates are better than the ones obtained by Kokoszka and Leipus (Stat. Probab. Lett., 1998, 40, 385-393). In order to illustrate our results, we do perform simulations based on m-AANA sequences. As important applications, we use the CUSUM-type estimator to do the change-point analysis based on three real data such as Quebec temperature, Nile flow, and stock returns for Tesla. Some potential applications to change-point models in finance and economics are also discussed in this paper.