非平稳Hawkes过程的序列检测

Moinak Bhaduri, D. Rangan, Anurag Balaji
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引用次数: 0

摘要

检测传入数据流中的更改对于理解固有依赖关系、制定新的或调整现有策略以及预测进一步的更改非常重要。不同的建模构造触发了检测这些变化的各种方法,几乎每一种方法都有一定的缺点。例如,基于时间序列对象的参数化模型在分布假设下或当对特定属性(如平均值、方差、趋势等)的变化检测感兴趣时工作得很好。其他算法严重依赖于“最多一个变化点”的假设,实现二值分割来发现后续的变化需要大量的计算成本。这项工作提供了另一种选择,既通用又不受这些令人窒息的限制。检测是通过对某些趋势排列统计的变化进行一系列测试来完成的。我们研究了非平稳Hawkes模式,它具有潜在的随机强度,暗示着一个自然的分支过程结构。我们的建议被证明可以有效地估计移民和后代强度的变化,而不会产生太多的误报。与已建立的竞争对手的比较揭示了更小的基于hausdorff的估计误差,理想的推理性质,如渐近一致性和更窄的自举边际。分析了纳斯达克价格走势、原油价格、海啸发生和COVID-19感染等4个真实数据集。预测方法也有涉及。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Change detection in non-stationary Hawkes processes through sequential testing
Detecting changes in an incoming data flow is immensely crucial for understanding inherent dependencies, formulating new or adapting existing policies, and anticipating further changes. Distinct modeling constructs have triggered varied ways of detecting such changes, almost every one of which gives in to certain shortcomings. Parametric models based on time series objects, for instance, work well under distributional assumptions or when change detection in specific properties - such as mean, variance, trend, etc. are of interest. Others rely heavily on the “at most one change-point” assumption, and implementing binary segmentation to discover subsequent changes comes at a hefty computational cost. This work offers an alternative that remains both versatile and untethered to such stifling constraints. Detection is done through a sequence of tests with variations to certain trend permuted statistics. We study non-stationary Hawkes patterns which, with an underlying stochastic intensity, imply a natural branching process structure. Our proposals are shown to estimate changes efficiently in both the immigrant and the offspring intensity without sounding too many false positives. Comparisons with established competitors reveal smaller Hausdorff-based estimation errors, desirable inferential properties such as asymptotic consistency and narrower bootstrapped margins. Four real data sets on NASDAQ price movements, crude oil prices, tsunami occurrences, and COVID-19 infections have been analyzed. Forecasting methods are also touched upon.
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