Correct and efficient estimation of the Hurst parameter H of long-range dependent (LRD) traffic is important in traffic analysis. The low computational cost and the wavelets' scale invariance make wavelet transform suitable for analysis of LRD processes. In this thesis, we apply wavelet-based estimation of H to MPEG-1 and MPEG-4 encoded video sequences. Frequency-domain estimators (periodogram and wavelet-based) produce different Hurst parameters compared to time-domain estimators (R/S and variance-time plot). Wavelet-based estimators often produce Hurst parameters that are close to or greater than one. Our analysis indicates that a possible cause for the unreliable performance of the wavelet-based estimators is the non-stationarity of the scaling exponent. We also apply the monofractal wavelet-based estimator to traces of call holding and call inter-arrival times collected from a circuit-switched cellular wireless network. We test the time constancy of the scaling exponent alpha and compare the estimates of H from various time periods.
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