A fluctuation test for constant correlation

Abstract

We propose a new test for constant correlation. It bases on successively estimated correlations and compares these with the estimated correlation of the whole data set. In contrast to existing tests for this problem, our test does not require that possible change points are known or that there is normality in the data. To derive the asymptotic null distribution, we develop a generalized delta-method on function spaces. Here, the considered random function is not multiplied by a scalar, but by another function. To achieve this, we generalize the concept of Hadamard differentiability. We show analytically that the test has non-trivial power against local alternatives. A simulation study confirms our analytical findings.