Partial Wavelet Canonical Coherence for Nonstationary Signals with High Dimensional Confounders

We develop Partial Wavelet Canonical Coherence for measuring the direct canonical association between two multivariate nonstationary time series after adjustment for possibly high-dimensional confounders. To the best of our knowledge, this is the first method that establishes a frequency-domain formulation of the partial canonical correlation analysis for time series. Through a wavelet approach, the proposed method yields a scale-specific, time-varying measure of association capable to work with potential data nonstationarities. We formulate the target quantity under the multivariate locally stationary wavelet framework, develop principled estimation through local wavelet spectral matrices, and incorporate principal-component reduction for stable adjustment in high-dimensions. Simulations show that the method removes spurious marginal association induced by confounding and accurately recovers direct association, including in higher-dimensional settings. Analysis of U.S. exchange-traded funds reveals substantial time-varying and scale-dependent direct canonical association after adjustment for external market effects.