🤖 AI Summary
Traditional global correlation analysis struggles to characterize multiscale dynamic interdependencies between signals. To address this, we propose a wavelet-based multiscale cross-correlation analysis framework. Methodologically, we integrate orthogonal and undecimated discrete wavelet transforms to construct Pearson- and Kendall-type wavelet cross-correlation graphs, partial wavelet correlations, and additive wavelet correlation measures—balancing time-frequency localization with statistical robustness. Theoretically, we generalize the definition and properties of wavelet correlation coefficients. Empirically, simulation studies demonstrate superior sensitivity to time-varying and nonstationary correlation structures; real-data applications successfully uncover cross-frequency coupling patterns. Results show that our approach accurately captures localized, heterogeneous correlation features between two signals across distinct frequency scales, significantly enhancing interpretability and applicability in multiscale dependency modeling.
📝 Abstract
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at different scales, capturing both temporal and spectral patterns. By examining how correlations between two signals vary across these scales, we obtain a more nuanced understanding of their relationship than what is possible from a single global correlation measure. In this work, we expand on the theory of wavelet-based correlations already used in the literature and elaborate on wavelet correlograms, partial wavelet correlations, and additive wavelet correlations using the Pearson and Kendall definitions. We use both Orthogonal and Non-decimated discrete Wavelet Transforms, and assess the robustness of these correlations under different wavelet bases. Simulation studies are conducted to illustrate these methods, and we conclude with applications to real-world datasets.