A new test of independence between random elements is presented in this article. The test is based on a functional of the Cramer-von Mises type, which is applied to a $U$-process that is defined from the recurrence rates. Theorems of asymptotic distribution under $H_{0},$ and consistency under a wide class of alternatives are obtained. The results under contiguous alternatives are also shown. The test has a very good behaviour under several alternatives, which shows that in many cases there is clearly larger power when compared to other tests that are widely used in literature. In addition, the new test could be used for discrete or continuous time series.

中文翻译：

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基于复发率的独立性测试

本文介绍了随机元素之间独立性的新测试。该检验基于 Cramer-von Mises 类型的泛函，该泛函应用于从重复率定义的 $U$ 过程。获得了在$H_{0}下的渐近分布定理和在广泛的备选方案下的一致性。还显示了连续替代项下的结果。该检验在多个备选方案下具有非常好的行为，这表明与文献中广泛使用的其他检验相比，在许多情况下显然具有更大的功效。此外，新测试可用于离散或连续时间序列。