A wavelet-based joint estimator of the parameters of long-range dependence

Abstract

Abstract-A joint estimator is presented for the two parameters that define the long-range dependence phenomenon in the simplest case. The estimator is based on the coefficients of a discrete wavelet decomposition, improving a recently proposed wavelet-based estimator of the scaling parameter [4], as well as extending it to include the associated power parameter. An important feature is its conceptual and practical simplicity, consisting essentially in measuring the slope and the intercept of a linear fit after a discrete wavelet transform is performed, a very fast (O(n)) operation. Under well-justified technical idealizations the estimator is shown to be unbiased and of minimum or close to minimum variance for the scale parameter, and asymptotically unbiased and efficient for the second parameter. Through theoretical arguments and numerical simulations it is shown that in practice, even for small data sets, the bias is very small and the variance close to optimal for both parameters. Closed-form expressions are given for the covariance matrix of the estimator as a function of data length, and are shown by simulation to be very accurate even when the technical idealizations are not satisfied. Comparisons are made against two maximum-likelihood estimators. In terms of robustness and computational cost the wavelet estimator is found to be clearly superior and statistically its performance is comparable. We apply the tool to the analysis of Ethernet teletraffic data, completing an earlier study on the scaling parameter alone.Index Terms-Hurst parameter, long-range dependence, packet traffic, parameter estimation, telecommunications networks, time-scale analysis, wavelet decomposition.

A wavelet lifting approach to long-memory estimation

“…As E{log(·)} = log{E(·)}, we correct for the bias introduced by regressing log 2 quantities in step A-4 using the same weighting as proposed by Veitch and Abry (1999), hence accounting for the different variability across artificial levels. The weights are obtained under the Gaussianity assumption, though Veitch and Abry (1999) report insensitivity to departures from this assumption.…”

“…Decorrelation is important for long-memory parameter estimation as taking the wavelet transform produces coefficients that are "quasidecorrelated," see Flandrin (1992) and Veitch and Abry (1999), Property P2, page 880. The decorrelation, and consequent removal of the long memory, then permits the use of established methods for long-memory parameter estimation using the lifting coefficients.…”

“…The weights are obtained under the Gaussianity assumption, though Veitch and Abry (1999) report insensitivity to departures from this assumption.…”

Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

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Multicast Transport Protocol Analysis: Self-Similar Sources

“…On the average, 50 messages per second are transmitted like the cbr simulations of [5]. In order to estimate the Hurst parameter H from the delay of these messages or from traffic counts at the link level, we apply the wavelet estimation method as given in [9] using Daubechies wavelets with three vanishing moments.…”