🤖 AI Summary
本文针对金融市场的不稳定性，提出基于修正Hankel变换和Laplace变换的两类新的非参数变点检测方法，并通过模拟和实际数据验证了其有效性。
📝 Abstract
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.