# An Independence Test Based on Recurrence Rates

## TL;DR

This paper introduces a new independence test based on recurrence rates and a Cramér-von Mises type functional, demonstrating strong asymptotic properties and higher power compared to existing tests, applicable to both discrete and continuous time series.

## Contribution

The paper presents a novel independence test leveraging recurrence rates and a U-process, with proven asymptotic distribution, consistency, and superior power in various scenarios.

## Key findings

- Test shows good behavior under multiple alternatives.
- Higher power compared to traditional independence tests.
- Applicable to both discrete and continuous time series.

## Abstract

A new test of independence between random elements is presented in this article. The test is based on a functional of the Cram\'{e}r-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.