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.

翻译：本研究首次提出了一类用于检测独立矩阵值随机变量序列分布变化点的检验方法。该检验基于经验正交汉克尔变换的加权平方积分差构建，其检验统计量具有便捷的闭式表达式，便于实际应用。我们给出了这些统计量的极限性质，并通过广泛模拟研究验证了其有效性。为展示其实用价值，我们将该检验应用于加密货币市场的变点检测。在此背景下识别变化点，可为新型交易系统的构建与分析提供多维度应用场景。