This paper aims to provide non-parametric tests for asymmetric comovements between random variables. We consider the popular Cramér-von Mises and Kolmogorov–Smirnov test statistics based on the distance between positive and negative joint conditional exceedance distribution functions. These tests can capture both linear and nonlinear dependence in the data and do not require selecting kernel functions and bandwidths. We derive the asymptotic distributions of the tests and establish the validity of a block multiplier-type bootstrap that one can use in finite-sample settings. We also show that these tests are consistent for any fixed alternative and have non-trivial power for detecting local alternatives converging to the null at the parametric rate. Monte Carlo simulations and a real financial data analysis illustrate satisfactory performance of the proposed tests.

中文翻译：

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不对称联动测试*

本文旨在为随机变量之间的非对称联动提供非参数检验。我们根据正负联合条件超出分布函数之间的距离来考虑流行的 Cramér-von Mises 和 Kolmogorov-Smirnov 检验统计量。这些测试可以捕获数据中的线性和非线性相关性，并且不需要选择核函数和带宽。我们推导出测试的渐近分布，并确定可以在有限样本设置中使用的块乘法器类型引导程序的有效性。我们还表明，这些测试对于任何固定替代方案都是一致的，并且对于检测以参数速率收敛到零的局部替代方案具有非平凡的能力。