Abstract

: Recent measurements of various types of network traffic have shown evidence consistent with long-range dependence and self-similarity. However, an alternative explanation for these measurements is non-stationarity in the data. Standard estimators of LRD parameters such as the Hurst parameter H assume stationarity and are susceptible to bias when this assumption does not hold. Hence LRD may be indicated by these estimators when none is present, or alternatively LRD taken to be non-stationarity. The recently developed Abry-Veitch (AV) joint estimator has much better properties when a time-series is non-stationary. In particular the effect of polynomial trends in data may be intrinsically eliminated from the estimates of LRD parameters. This paper investigates the behavior of the AV estimator when there are non-stationarities in the form of a level shift in the mean and/or the variance of a process. We examine cases where the change occurs both gradually or as a single jump discontinuit...

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