Wavelet scale analysisof bivariate time series ii:statistical properties for linear processes

Scaling characteristics of stochastic processes can be examined using wavelet cross-co- variances. For jointly stationary but generally non-Gaussian linear processes, the asymptotic properties of the resulting wavelet cross-covariance estimator are derived. The linear processes are assumed to have only a square-summable weight sequence, so that the class of processes includes long-memory processes. The variance of the estimator can in each case be expressed as a spectrum value at zero frequency, and can hence be readily estimated. A simulation experiment is reported which demonstrates the utility of this approach. A comparison of estimated standard deviations of wavelet autocovar-iances and cross-covariances for Beaufort Sea albedo/temperature data under both Gaussian and non-Gaussian assumptions, illustrates the necessity of developing the non-Gaussian theory.