Tail Spectral Density Estimation and Its Uncertainty Quantification: Another Look at Tail Dependent Time Series Analysis
Tail Spectral Density Estimation and Its Uncertainty Quantification: Another Look at Tail Dependent Time Series Analysis
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DOI：
10.1080/01621459.2023.2197159
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发表时间：
2023-03
影响因子：
3.7
通讯作者：
Ting Zhang;Beibei Xu
中科院分区：
文献类型：
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作者：
Ting Zhang;Beibei Xu
考虑尾谱密度的估计和不确定性量化，为尾相关时间序列的尾谱分析提供基础。尾谱密度特别关注尾部的序列依赖性，可以揭示传统谱分析无法发现的依赖性信息。然而，了解尾谱密度估计器的收敛速度并找到量化其统计不确定性的严格方法仍然是一个悬而未决的问题。本文旨在填补这一空白，提供了一种新的关于尾统计二次型在双渐近设置下的渐近理论，在此基础上，我们发展了尾谱密度估计的一致性和期望已久的中心极限定理。然后将结果用于设计一种简洁有效的方法来构建置信区间，以测量尾谱密度估计器的统计不确定性，并且可以将其转化为可视化工具，以帮助从业者检查其感兴趣的数据的尾部依赖性。给出了包括数据应用在内的数值算例来说明所得到的结果。本文的补充材料可在网上获得。
Abstract We consider the estimation and uncertainty quantification of the tail spectral density, which provide a foundation for tail spectral analysis of tail dependent time series. The tail spectral density has a particular focus on serial dependence in the tail, and can reveal dependence information that is otherwise not discoverable by the traditional spectral analysis. Understanding the convergence rate of tail spectral density estimators and finding rigorous ways to quantify their statistical uncertainty, however, still stand as a somewhat open problem. The current article aims to fill this gap by providing a novel asymptotic theory on quadratic forms of tail statistics in the double asymptotic setting, based on which we develop the consistency and the long desired central limit theorem for tail spectral density estimators. The results are then used to devise a clean and effective method for constructing confidence intervals to gauge the statistical uncertainty of tail spectral density estimators, and it can be turned into a visualization tool to aid practitioners in examining the tail dependence for their data of interest. Numerical examples including data applications are presented to illustrate the developed results. Supplementary materials for this article are available online.