Segmenting time series via self‐normalisation
Segmenting time series via self‐normalisation
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DOI：
10.1111/rssb.12552
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Zifeng Zhao;Feiyu Jiang;Xiaofeng Shao
中科院分区：
文献类型：
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作者：
Zifeng Zhao;Feiyu Jiang;Xiaofeng Shao
我们提出了一个新的、统一的多变量时间序列变点估计框架。所提出的方法是完全非参数的，对时间相关性具有鲁棒性，并且避免了对长期方差的一致性估计的要求。该方法的一个显著和独特的特点是它的通用性，它允许以统一的方式对一大类参数(如均值、方差、相关性和分位数)进行变点检测。在我们方法的核心，我们将基于自归一化(SN)的测试与一种新的嵌套局部窗口分割算法结合在一起，这在不断增长的变点分析文献中似乎是新的。由于SN检验中存在不一致的长期方差估计，进一步发展了非标准的理论论证，推导了基于SN的变点检测方法的一致性和收敛速度。通过大量的数值实验和相关的真实数据分析，证明了该方法的有效性和广泛的适用性，并与文献中最先进的方法进行了比较。
We propose a novel and unified framework for change‐point estimation in multivariate time series. The proposed method is fully non‐parametric, robust to temporal dependence and avoids the demanding consistent estimation of long‐run variance. One salient and distinct feature of the proposed method is its versatility, where it allows change‐point detection for a broad class of parameters (such as mean, variance, correlation and quantile) in a unified fashion. At the core of our method, we couple the self‐normalisation‐ (SN) based tests with a novel nested local‐window segmentation algorithm, which seems new in the growing literature of change‐point analysis. Due to the presence of an inconsistent long‐run variance estimator in the SN test, non‐standard theoretical arguments are further developed to derive the consistency and convergence rate of the proposed SN‐based change‐point detection method. Extensive numerical experiments and relevant real data analysis are conducted to illustrate the effectiveness and broad applicability of our proposed method in comparison with state‐of‐the‐art approaches in the literature.