Decorrelation of Wavelet Coefficients for Long-Range Dependent Processes

We consider a discrete-time stationary long-range dependent process (X_k)_kisinZ such that its spectral density equals phi(|lambda|)^-2d, where phi is a smooth function such that phi(0)=phi´´(0)=0 and phi(lambda)gesclambda for lambdaisin[0,pi]. Then for any wavelet psi with N vanishing moments, the lag k within-level covariance of wavelet coefficients decays as O(k^2d-2N-1) when krarrinfin. The result applies to fractionally integrated autoregressive moving average (ARMA) processes as well as to fractional Gaussian noise