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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Saisai Ding & Xiaoqin Li & Xiang Dong & Wenzhi Yang, 2020. "The Consistency of the CUSUM-Type Estimator of the Change-Point and Its Application," Mathematics, MDPI, vol. 8(12), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2113-:d:451374
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    References listed on IDEAS

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    1. Michael Messer & Stefan Albert & Gaby Schneider, 2018. "The multiple filter test for change point detection in time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 589-607, August.
    2. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    3. Kokoszka, Piotr & Leipus, Remigijus, 1998. "Change-point in the mean of dependent observations," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 385-393, November.
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