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Inference for mean change-point in infinite variance AR(p) process

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  • Zhou, Jie
  • Liu, San Y.

Abstract

In this paper a weighted least square method is proposed to infer the change-point in AR(p) process with infinite variance, and a weighted cumulative sum statistic (CUSUM) is obtained. Based on the weighted CUSUM statistic the distribution of the test statistic is derived. The consistency and the rate of convergence for the weighted CUSUM estimator are also established. The simulation results support the validity of such a weighted CUSUM estimator.

Suggested Citation

  • Zhou, Jie & Liu, San Y., 2009. "Inference for mean change-point in infinite variance AR(p) process," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 6-15, January.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:1:p:6-15
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    References listed on IDEAS

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    1. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    2. Shiqing Ling, 2005. "Self‐weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393, June.
    3. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
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    Cited by:

    1. Qin, Ruibing & Tian, Zheng & Jin, Hao & Zhang, Xiaowei, 2010. "Strong convergence rate of robust estimator of change point," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2026-2032.

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