Change point in variance of fractionally integrated noise

Daiqing Xi () and Tianxiao Pang ()
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Daiqing Xi: Zhongnan University of Economics and Law
Tianxiao Pang: Zhejiang University

Statistical Papers, 2024, vol. 65, issue 4, No 19, 2397-2439

Abstract: 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

Keywords: Change point in variance; Fractionally integrated noise; Long memory; Quasi-maximum likelihood estimator; Rosenblatt process; 62F10; 62F12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01490-5

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