Wavelet coefficients cross-correlation analysis of times series

The discrete wavelet transform (DWT) is becoming very widely used in the analysis of discrete time stochastic processes. In this paper we explore the maximal overlap discrete wavelet transform (MODWT) which carries out the same filtering steps as the ordinary DWT but does not subsample by 2, and is well defined for any sample size. We address the problem of examining the wavelet auto and cross-correlation structure between wavelet coefficients at different scales of a time series. We construct an estimator of this quantity based on wavelets coefficients. The asymptotic distribution of this estimator is derived for a wide class of stochastics processes. A simulation experiment is reported which demonstrates how the cross-correlation is spreaded out over higher scales for linear and nonlinear processe