Abstract

Quantifying dependence is a central theme in statistics. Classical measures such as Pearson’s correlation coefficient, Spearman’s rho, Kendall’s tau, and more recent Chatterjee’s correlation illustrate that an appropriate concept of dependence and its quantification depend on the context and purpose. For the situation where marginal distributions are assumed to be identical, we propose a new measure of dependence which is invariant under any identical transformation applied to both marginals. We call this measure the maximal autocorrelation coefficient. This coefficient can be viewed as a variant of the well-known Renyi’s maximal correlation, specialized to the case of identical marginals. When the marginals are continuous, this measure depends only on the underlying copula. Based on the discretization of transformations, we develop an algorithm to compute this maximal autocorrelation. To demonstrate the usefulness of this measure, we provide an application of this correlation coefficient to detect hidden serial dependence structures in time series.