基于球检测函数的多元时间序列分层变点检测
Hierarchical Change-Point Detection for Multivariate Time Series via a Ball Detection Function
摘要：
随机目标序列来源于许多实际应用，包括高通量的组学数据和功能成像数据。这些序列通常是相依的、非线性的、甚至是非欧的，在巴拿赫空间或度量空间中，这类相依序列的变点检测是一个重要的问题。该问题通常不仅需要准确推断是否发生了变化，而且还需要准确推断变化发生时的位置。为此，我们首先介绍了球检测功能，并表明，它达到最大值的变化点，如果一个序列只有一个变化点。此外，我们提出了一个一致的估计球检测功能的基础上，我们开发了一个分层算法来检测所有可能的变化点。我们证明了估计的变点位置是一致的。我们的程序可以估计的数量变化点，并检测其位置，而不假设任何特定类型的变化点，因为变化可以发生在一个序列中以不同的方式。对两个有趣的真实数据集风向和比特币价格的广泛模拟研究和分析表明，我们的方法比现有的竞争对手具有相当大的优势，特别是当数据是非欧几里德或方差存在分布变化时。
英文摘要：
Sequences of random objects arise from many real applications, including high throughput omic data and functional imaging data. Those sequences are usually dependent, non-linear, or even Non-Euclidean, and an important problem is change-point detection in such dependent sequences in Banach spaces or metric spaces. The problem usually requires the accurate inference for not only whether changes might have occurred but also the locations of the changes when they did occur. To this end, we first introduce a Ball detection function and show that it reaches its maximum at the change-point if a sequence has only one change point. Furthermore, we propose a consistent estimator of Ball detection function based on which we develop a hierarchical algorithm to detect all possible change points. We prove that the estimated change-point locations are consistent. Our procedure can estimate the number of change-points and detect their locations without assuming any particular types of change-points as a change can occur in a sequence in different ways. Extensive simulation studies and analyses of two interesting real datasets wind direction and Bitcoin price demonstrate that our method has considerable advantages over existing competitors, especially when data are non-Euclidean or when there are distributional changes in the variance.
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