Ten lectures on wavelets
On the self-similar nature of Ethernet traffic
ACM SIGCOMM Computer Communication Review - Special twenty-fifth anniversary issue. Highlights from 25 years of the Computer Communication Review
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Proof of a fundamental result in self-similar traffic modeling
ACM SIGCOMM Computer Communication Review
Meaningful MRA intitialization for discrete time series
Signal Processing - Special issue on current topics in adaptive filtering for hands-free acoustic communication and beyond
Self-Similar Network Traffic and Performance Evaluation
Self-Similar Network Traffic and Performance Evaluation
Estimation of the self-similarity parameter in linear fractional stable motion
Signal Processing - Signal processing with heavy-tailed models
Wavelet analysis of long-range-dependent traffic
IEEE Transactions on Information Theory
A wavelet-based joint estimator of the parameters of long-range dependence
IEEE Transactions on Information Theory
Correlation structure of the discrete wavelet coefficients of fractional Brownian motion
IEEE Transactions on Information Theory - Part 2
Estimation of Hurst exponent revisited
Computational Statistics & Data Analysis
Visualization and inference based on wavelet coefficients, SiZer and SiNos
Computational Statistics & Data Analysis
Editorial: 2nd Special Issue on Statistical Signal Extraction and Filtering
Computational Statistics & Data Analysis
Global modeling of backbone network traffic
INFOCOM'10 Proceedings of the 29th conference on Information communications
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The Hurst parameter H characterizes the degree of long-range dependence (and asymptotic self-similarity) in stationary time series. Many methods have been developed for the estimation of H from data. In practice, however, the classical estimation techniques can be severely affected by non-stationary artifacts in the time series. In fact, the assumption that the data can be modeled by a stationary process with a single Hurst exponent H may be unrealistic. This work focuses on practical issues associated with the detection of long-range dependence in Internet traffic data and proposes two tools that can be used to address some of these issues. The first is an animation tool which is used to visualize the local dependence structure. The second is a statistical tool for the local analysis of self-similarity (LASS). The LASS tool is designed to handle time series that have long-range dependence and are long enough that some parts are essentially stationary, while others exhibit non-stationarity, which is either deterministic or stochastic in nature. The tool exploits wavelets to analyze the local dependence structure in the data over a set of windows. It can be used to visualize local deviations from self-similar, long-range dependence scaling and to provide reliable local estimates of the Hurst exponents. The tool, which is illustrated by using a trace of Internet traffic measurements, can also be applied to economic time series. In addition, a median-based wavelet spectrum is introduced. It yields robust local or global estimates of the Hurst parameter that are less susceptible to local non-stationarity. The software tools are freely available and their use is described in an appendix.