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Change point in variance of fractionally integrated noise

Author

Listed:
  • Daiqing Xi

    (Zhongnan University of Economics and Law)

  • Tianxiao Pang

    (Zhejiang University)

Abstract

This paper studies the quasi-maximum likelihood estimator (quasi-MLE) of a change point in variance for the fractionally integrated noise with memory parameter $$d\in (-\,0.5,0.5)$$ d ∈ ( - 0.5 , 0.5 ) , and the asymptotic behaviors of the estimator are examined. We show that: (1) For the case of fixed break magnitude, the quasi-MLE of the change point is inconsistent, while that of the change-point fraction is T-consistent. (2) For the case of shrinking break magnitude, the intermediate memory dependency has no impact on the convergence rate of the quasi-MLE of the change point. However, it is not the case when the process is long-range dependent. Specifically, the asymptotic behaviors of the quasi-MLE of the change point vary from the case where $$0

Suggested Citation

  • Daiqing Xi & Tianxiao Pang, 2024. "Change point in variance of fractionally integrated noise," Statistical Papers, Springer, vol. 65(4), pages 2397-2439, June.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01490-5
    DOI: 10.1007/s00362-023-01490-5
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