Estimating the Hurst index of a self-similar process via the crossing tree

By considering the crossings of size 2ⁿ made by a continuous self-similar process, for n = ..., -1, 0, 1, ..., we build a tree of crossings that encodes the sample path. From the crossing tree, we obtain a test for self-similarity and an estimator for the Hurst index, H. The accuracy of the estimator is established theoretically and numerically, and a comparison study with three other estimators is given, demonstrating its superior performance. The estimator and self-similarity test are applied to network packet traces, revealing some previously unobserved features.