变点分析：不稳定金融市场的新视角
Change-point analysis: a new perspective for unstable financial markets
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中文总结 AI 辅助
该研究针对单变量非负随机变量序列，提出两类基于变换的非参数变点检验，经模拟和实际金融、气象数据验证，其检验功效与变点位置估计精度优于同类方法，可有效检测分布变化。
中文摘要 AI 辅助
我们针对单变量非负随机变量序列，引入两类新的非参数变点检验方法。所提方法分别基于经验修正汉克尔变换和拉普拉斯变换，为检测分布变化提供了新的基于变换的工具。我们推导了对应检验统计量的渐近零分布，并采用置换自助法获取p值，因为极限零分布不具有分布自由性。通过有限样本模拟研究表明，所提检验校准良好，总体上比基于经验特征函数的同类检验更具功效，且能准确估计变点位置，尤其在非对称场景中表现突出。阿根廷降雨量数据、美国国民生产总值（GNP）及标准普尔500指数（S&P 500）绝对对数收益率的应用进一步验证了所提方法的实用性，实例说明基于汉克尔变换和拉普拉斯变换的检验是检测非负数据中有意义分布变化的有效工具。
英文摘要
We introduce two new classes of nonparametric change-point tests for sequences of univariate non-negative random variables. The proposed procedures are based on the empirical modified Hankel transform and the Laplace transform, respectively, and provide new transform-based tools for detecting distributional changes. We derive the asymptotic null distributions of the corresponding test statistics and use a permutation bootstrap procedure to obtain $p$-values, since the limiting null distributions are not distribution-free. Through a finite-sample simulation study, we show that the proposed tests are well calibrated, generally more powerful than empirical-characteristic-function-based competitors, and capable of accurately estimating the change-point location, particularly in asymmetric settings. The usefulness of the proposed methodology is further demonstrated through applications to Argentina rainfall data, as well as U.S. GNP and S\&P 500 absolute log-returns. The real-data examples illustrate that the proposed Hankel- and Laplace-transform-based tests are effective tools for detecting meaningful distributional changes in non-negative data.
发表机构
- Faculty of Mathematics University of Belgrade（贝尔格莱德大学数学学院）
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