Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights
Modelling Short- and Long-Term Dependencies of Clustered High-Threshold Exceedances in Significant Wave Heights
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DOI：
10.3390/math9212817
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发表时间：
2021-11
期刊：
影响因子：
2.4
通讯作者：
P. Dissanayake;T. Flock;Johanna Meier;P. Sibbertsen
中科院分区：
文献类型：
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作者：
P. Dissanayake;T. Flock;Johanna Meier;P. Sibbertsen
超过阈值的峰值（POT）方法在模拟环境变量的极端情况方面有着悠久的传统。然而，它最初是在独立同分布（iid）数据的假设下引入的。由于环境数据往往表现出时间序列结构，这一假设很可能会被违反，由于短期和长期的依赖性，在实际设置，导致集群的高阈值不一致性。在本文中，我们首先回顾流行的方法，无论是专注于短期或长期动态建模明确。特别是，我们认为有条件的POT的变种和Mittag-Leffler分布建模之间的等待时间。此外，我们提出了一个新的两步方法，同时捕获短期和长期的相关性。我们建议自回归分数积分移动平均峰值超过阈值（ARFIMA-POT）的方法，在第一步适合ARFIMA模型的原始系列，然后在第二步利用经典的POT模型的残差。应用这些模型的海洋学时间序列的显着波高测量的塞夫顿海岸（英国），我们发现，无论是单独建模短期或长期的依赖性令人满意地解释了集群的极端。然而，ARFIMA-POT方法在模型拟合方面提供了显着的改进，强调了需要将短期和长期依赖性结合起来以解决极值聚类的模型及其理论依据。
The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely to be violated due to short- and long-term dependencies in practical settings, leading to clustering of high-threshold exceedances. In this paper, we first review popular approaches that either focus on modelling short- or long-range dynamics explicitly. In particular, we consider conditional POT variants and the Mittag–Leffler distribution modelling waiting times between exceedances. Further, we propose a new two-step approach capturing both short- and long-range correlations simultaneously. We suggest the autoregressive fractionally integrated moving average peaks-over-threshold (ARFIMA-POT) approach, which in a first step fits an ARFIMA model to the original series and then in a second step utilises a classical POT model for the residuals. Applying these models to an oceanographic time series of significant wave heights measured on the Sefton coast (UK), we find that neither solely modelling short- nor long-range dependencies satisfactorily explains the clustering of extremes. The ARFIMA-POT approach, however, provides a significant improvement in terms of model fit, underlining the need for models that jointly incorporate short- and long-range dependence to address extremal clustering, and their theoretical justification.