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Quantile autocovariances: A powerful tool for hard and soft partitional clustering of time series

机译：分位数自协方差：用于时间序列的硬分区和软分区聚类的强大工具

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A key issue in cluster analysis is determining a proper dissimilarity measure between two data objects, and many pairwise dissimilarities have been proposed to deal with time series. Assuming that the clustering purpose is to group series according to the underlying dependence structures, a detailed study of the behavior in clustering of a dissimilarity based on comparing estimated quantile autocovariance functions (QAF) is carried out. Quantile autocovariances provide information about the serial dependence structure that other conventional features are not able to capture, which suggests great potential to perform clustering of series. The asymptotic behavior of the sample quantile autocovariances is studied and an algorithm to determine optimal combinations of lags and pairs of quantile levels to perform clustering is introduced. The proposed metric is used to perform hard and soft partitioning-based clustering. First, a broad simulation study examines the behavior of the proposed metric in crisp clustering with the PAM procedure. A novel fuzzy C-medoids algorithm based on the QAF-dissimilarity is then proposed and compared with other fuzzy procedures in a new simulation study conducted to cluster fuzzy scenarios involving AR and GARCH models. In all cases, the QAF-based procedures outperform or are highly competitive with a range of dissimilarities reported in the literature, particularly exhibiting high capability to cluster conditionally heteroskedastic time series and robustness to the distributional form of the errors. Two specific applications involving air quality data and financial time series illustrate the usefulness of the proposed procedures. (C) 2017 Elsevier B.V. All rights reserved.
机译：聚类分析中的一个关键问题是确定两个数据对象之间的适当差异度量，并且提出了许多成对的差异来处理时间序列。假设聚类的目的是根据潜在的依存结构对序列进行分组，则基于比较估计的分位数自协方差函数（QAF），对相异性聚类中的行为进行了详细研究。分位数自协方差提供有关其他传统功能无法捕获的序列依赖结构的信息，这表明执行序列聚类的潜力很大。研究了样本分位数自协方差的渐近行为，并引入了确定滞后和分位数对的最佳组合以进行聚类的算法。提出的度量标准用于执行基于硬分区和软分区的群集。首先，广泛的仿真研究使用PAM程序检查了建议度量在明晰聚类中的行为。然后提出了一种新的基于QAF不相似性的模糊C-medoids算法，并将其与其他模糊过程进行了比较，在一项新的仿真研究中对涉及AR和GARCH模型的模糊场景进行了聚类。在所有情况下，基于QAF的程序在文献中报道的一系列差异方面均优于或具有极强的竞争力，尤其表现出对条件异方差时间序列进行聚类的能力以及对错误的分布形式的鲁棒性。涉及空气质量数据和财务时间序列的两个特定应用程序说明了所建议程序的有用性。 （C）2017 Elsevier B.V.保留所有权利。

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