AI 中文总结
该研究提出一种角数据均值方向变化点的无分布检验，经模拟与基准测试验证其性能，还应用于加密货币与黄金价格极端事件时间戳分析，为金融领域角数据变化点检测提供新方法。
AI 中文摘要
本文提出一种用于检测角数据均值方向变化点的无分布检验方法。角测量的不确定性通过环面内在几何推导的“角的平方”量化。研究确定，在原假设下，检验统计量依分布收敛于柯尔莫哥洛夫分布；在备择假设下，确立了检验的一致性及变化点估计量的渐近性质。通过大量模拟，将所提方法与两种现有角数据方法的经验性能进行比较，并与基于圆弧长度距离的检验进行基准测试。最后，通过分析比特币、以太坊和黄金价格数据集的极端事件时间戳，证明了该方法的实际效用，其中数据的连续高频特性在圆形框架中建模。
英文摘要
In this paper, we propose a distribution-free test for detecting changepoint in the mean direction of angular data. The uncertainty in angular measurements is quantified through the \textit{square of an angle}, derived from the intrinsic geometry of the torus. It is established that, under the null hypothesis, the test statistic distributionally converges to the Kolmogorov distribution, while under the alternative hypothesis, both the consistency of the test and the asymptotic properties of the changepoint estimator are established. Through extensive simulations, we compare the empirical performance of the proposed method with two existing approaches for angular data and further benchmark it against a test based on the circular arc length distance. Finally, we demonstrate the practical utility of our approach by analyzing the timestamps of extreme events in Bitcoin, Ethereum, and Gold price datasets, where the continuous, high-frequency nature of the data is modeled in the circular framework.
