We propose a CUSUM type test for constant correlation that goes beyond a previously suggested correlation constancy test by considering Spearman's rho in arbitrary dimensions. By using copula-based expressions, we simultaneously extend a previously suggested copula constancy test. We calculate the asymptotic null distribution 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. We give a local power result and analyse the test's behaviour in small samples.
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