Asymptotics of sample tail autocorrelations for tail-dependent time series: phase transition and visualization
Asymptotics of sample tail autocorrelations for tail-dependent time series: phase transition and visualization
复制标题
尾部相关时间序列样本尾部自相关的渐近：相变和可视化
DOI：
10.1093/biomet/asab038
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发表时间：
2021
期刊：
影响因子：
2.7
通讯作者：
Zhang, Ting
中科院分区：
文献类型：
--
作者：
Zhang, Ting
在这篇文章中，我们发展了一个关于时间序列数据的样本尾部自相关的渐近理论，该序列数据在尾部和非尾部都表现出序列相关性。与传统的自相关函数不同，尾部自相关的研究需要一个双重渐近格式来捕捉尾部现象，并且我们的结果不会对非尾区的依赖结构施加任何限制，并且允许过程不一定是强混合的。新发展的渐近理论揭示了一个以前未发现的相变现象，当滞后指数超过序列尾部相关性消失的点时，样本尾部自相关的渐近行为，包括它们的收敛速度，可以从一个阶段转移到另一个阶段。相变发现填补了现有尾部自相关研究的一个空白，类似于传统的自相关图，可以用来构建有意义的线，当可视化样本尾部自相关来评估序列尾部相关性的存在或识别尾部相关性的最大滞后时。
In this article we develop an asymptotic theory for sample tail autocorrelations of time series data that can exhibit serial dependence in both tail and non-tail regions. Unlike with the traditional autocorrelation function, the study of tail autocorrelations requires a double asymptotic scheme to capture the tail phenomena, and our results do not impose any restrictions on the dependence structure in non-tail regions and allow processes that are not necessarily strongly mixing. The newly developed asymptotic theory reveals a previously undiscovered phase transition phenomenon, where the asymptotic behaviour of sample tail autocorrelations, including their convergence rate, can transition from one phase to another as the lag index moves past the point beyond which serial tail dependence vanishes. The phase transition discovery fills a gap in existing research on tail autocorrelations and can be used to construct the lines of significance, in analogy to the traditional autocorrelation plot, when visualizing sample tail autocorrelations to assess the existence of serial tail dependence or to identify the maximal lag of tail dependence.