Fast real-time Hurst parameter estimation via adaptive wavelet lifting

A new real-time estimator of the Hurst parameter of a long-range dependent process is developed based on the lifting scheme for wavelet transform. Compared with the existing wavelet-based estimator, the new method performs inplace computation and reduces the computational complexity by about half. We also propose a median-based nonlinear lifting scheme to mitigate the border effects and the noise in the data, by adaptively adjusting the number of vanishing moments of the wavelet. The proposed algorithms are applied to estimate the Hurst parameters in two types of long-range dependent processes, namely, the multiple-access interference in a code-division multiple-access packet data network, and the measurement data of Internet traffic.