Decorrelation of Wavelet Coefficients for Long-Range Dependent Processes

Authors:
J. Mielniczuk;P. Wojdyllo
Affiliations:
Inst. of Comput. Sci., Polish Acad. of Sci., Warsaw;-
Venue:
IEEE Transactions on Information Theory
Year:
2007

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IEEE Transactions on Communications

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Abstract

We consider a discrete-time stationary long-range dependent process (Xk)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(k2d-2N-1) when krarrinfin. The result applies to fractionally integrated autoregressive moving average (ARMA) processes as well as to fractional Gaussian noise