Hurst Parameter Estimation from Noisy Observations of Data Trafc Traces

Abstract: Data trafc traces are known to be bursty with long range dependence. The exact self-similarity model of long range dependence can pose analytical and practical problems at very small and very large time lags. In our model, the time series of the trafc trace (referred to as the signal) is assumed to possess an autocovariance prole corresponding to exact self-similarity over a range of lags, fkg, satisfying M < k < L. At lower lags, exact self-similarity may breakdown, or additive moving average type noise (inaccuracies) may corrupt the autocovariances. At very high lags, far beyond the number of observed samples, the autocovariance structure is irrelevant and may be assumed to be innite summable. Therefore, L can be as large as desired. Applications of such a model are discussed. The mean, variance, and the Hurst parameter of the signal, as well as the autocovariances of any independent zero mean moving average type additive noise are assumed to be unknown. A class of linear combinations of sample average second order statistics of noisy observations is constructed. They are unbiased estimates of their corresponding expectations. These expectations are shown to be devoid of the noise statistics. The ratio of two such expectations eliminates the signal variance. The ratio is a well behaved monotonic function of the only remaining unknown, the Hurst parameter. Equating the ratio of these expectations to the ratio of the corresponding sample averages from the noisy observations leads to a very easily solvable nonlinear equation with a unique root. The result and related issues are discussed