On the Phase Dependence in Time-Varying Correlations between Time-Series

This paper proposes the use of a double correlation coefficient as a nonpara- metric measure of phase-dependence in time-varying correlations. An asymp- totically Gaussian test statistic for the null hypothesis of no phase-dependence is derived from the proposed measure. Finite-sample distributions, power and size are analyzed in a Monte-Carlo exercise. An application of this test provides evidence that correlation strength between major macroeconomic aggregates is both time-varying and phase dependent in the business cycle.