The Scale Analysis of Bivariate Non-gaussian Time Series via Wavelet Cross-covariance

Many scientiic studies require a thorough understanding of the scaling characteristics of observed processes. We derive and justify a decomposition of the usual cross-covariance in terms of scale-by-scale wavelet cross-covariances, and provide an estimator of the wavelet cross-covariance at speciied lag. For jointly stationary but generally non-Gaussian linear processes, asymptotic results are given for this wavelet cross-covariance estimator. The variance of the esimator can in each case be expressed as a spectrum value at zero frequency, a convenient form for practical estimation. A detailed scale analysis of the surface albedo and temperature of pack ice in the Beaufort Sea ably demonstrates the usefulness of wavelet analysis in decomposing structures at diierent scales hidden in time series data.