变点分析——经验Hankel变换方法
Change point analysis -- the empirical Hankel transform approach
AI总结：
本研究首次提出基于经验正交Hankel变换的检验方法，用于检测矩阵值随机变量序列的变点，并通过模拟和加密货币市场数据验证其有效性。
摘要：
在本研究中，我们首次引入了一类用于检测独立矩阵值随机变量序列分布中变点的检验方法。这些检验基于经验正交Hankel变换的加权平方积分差构建。检验统计量具有便捷的闭式表达式，使其在实践中易于实现。我们给出了其极限性质，并通过广泛的模拟研究展示了其优良性能。我们利用这些检验对加密货币市场中的变点进行检测，以展示其实际应用。在此背景下检测变点可为构建和分析新型交易系统提供多种应用。
英文摘要：
In this study, we introduce the first-of-its-kind class of tests for detecting change points in the distribution of a sequence of independent matrix-valued random variables. The tests are constructed using the weighted square integral difference of the empirical orthogonal Hankel transforms. The test statistics have a convenient closed-form expression, making them easy to implement in practice. We present their limiting properties and demonstrate their quality through an extensive simulation study. We utilize these tests for change point detection in cryptocurrency markets to showcase their practical use. The detection of change points in this context can have various applications in constructing and analyzing novel trading systems.
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