A fluctuation test for constant Spearman's rho with nuisance-free limit distribution

TL;DR

This paper introduces a new fluctuation test for constant Spearman's rho that is applicable to heavy-tailed data, with a nuisance-free limit distribution, enabling easier and more reliable testing of correlation constancy.

Contribution

It develops a CUSUM type test for Spearman's rho that does not require moment conditions and provides a nuisance-free asymptotic null distribution.

Findings

Test is applicable to heavy-tailed financial data.

Limit distribution is free of nuisance parameters.

Critical values can be obtained without bootstrap.

Abstract

A CUSUM type test for constant correlation that goes beyond a previously suggested correlation constancy test by considering Spearman's rho in arbitrary dimensions is proposed. Since the new test does not require the existence of any moments, the applicability on usually heavy-tailed financial data is greatly improved. The asymptotic null distribution is calculated using an invariance principle for the sequential empirical copula process. The limit distribution is free of nuisance parameters and critical values can be obtained without bootstrap techniques. A local power result and an analysis of the behavior of the test in small samples is provided.