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

Saisai Ding (), Xiaoqin Li (), Xiang Dong () and Wenzhi Yang ()
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Saisai Ding: School of Mathematical Sciences, Anhui University, Hefei 230601, China
Xiaoqin Li: School of Mathematical Sciences, Anhui University, Hefei 230601, China
Xiang Dong: School of Life Sciences, Anhui University, Hefei 230601, China
Wenzhi Yang: School of Mathematical Sciences, Anhui University, Hefei 230601, China

Mathematics, 2020, vol. 8, issue 12, 1-12

Abstract: 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 α − 1 ) , where 0 ≤ α < 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.

Keywords: CUSUM estimator; change-point; financial time series; negatively associated sequences (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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