Multi-scale analysis of univariate time series has appeared in the literature at an ever increasing rate. Here we introduce the multi-scale analysis of covariance between two time series using the discrete wavelet transform. The wavelet covariance and wavelet correlation are defined and applied to this problem as an alternative to traditional cross-spectrum analysis. The wavelet covariance is shown to decompose the covariance between two stationary processes on a scale by scale basis.
Asymptotic normality is established for estimators of the wavelet covariance and correlation.