Wavelet Packet Transform for Fractional Brownian Motion: Asymptotic Decorrelation and Selection of Best Bases

Our first goal in this paper is to investigate stationarization and asymptotic decorrelation for fractional Brownian motion (fBm) using wavelet packet transform. The wavelet packets are generated by the Nth-order Daubechies scaling function and wavelet. To decorrelate the wavelet packet coefficients asymptotically, we take two strategies: fix N and let absolute scale difference or absolute difference between time shifts get large; and fix scale level and time shift and let N get large. Our second goal is to present the asymptotic properties of the entropy-like cost functional and denoising cost functional and their impact on the selection of best wavelet packet bases when used for fBm plus or not plus independent Gaussian white noise.