Long-Range Dependence: Now you see it, now you don’t!

Over the last few years, the network community has started to make heavy use of novel concepts such as self-similarity and Long-Range Dependence (LRD). Despite their wide use, there is still much confusion regarding the identification of such phenomena in real network traffic data. In this paper, we show that estimating Long-Range Dependence is not straightforward: there is no systematic or definitive methodology. There exist several estimating methodologies, but they can give misleading and conflicting estimates. More specifically, we arrive at several conclusions that could provide guidelines for a systematic approach to LRD. First, long-range dependence may exist even, if the estimators have different estimates of the Hurst exponent in the interval 0.5-1. Second, long-range dependence is unlikely to exist, if there are several estimators that fail to estimate the Hurst exponent. Third, we show that periodicity can obscure the analysis of a signal giving partial evidence of long-range dependence. Fourth, the Whittle estimator is the most accurate in finding the exact value when LRD exists, but it can be fooled easily by periodicity. As a case-study, we analyze real round-trip time data. We find and remove a periodic component from the signal, before we can identify long-range dependence in the remaining signal.