Long-Range Dependence

  • Paul Doukhan
Part of the Mathématiques et Applications book series (MATHAPPLIC, volume 80)


Long-range dependent (LRD) phenomena were first exhibited by Hurst for hydrology purposes. This phenomenon occurs from the superposition of independent sources, e.g. confluent rivers provide this behaviour (see Fig.  4.2). Such aggregation procedures provide this new phenomenon. Hurst (Trans Am Soc Civ Eng 116:770–799, 1951) originally determined the optimum dam sizing for the Nile river’s volatile rain and drought conditions observed over a long period of time. LRD is characterized by slow decorrelation properties and the behaviour of partial sums’s variances. This phenomenon is discussed above, see Sects.  4.3 and  4.4. Asymptotic properties of instantaneous functions of Gaussian processes are provided in Remark  5.2.4. Infinite moving averages models with LRD properties are provided in Sects.  6.4 and  6.6. We refer the reader to Doukhan et al. (Theory and applications of long-range dependence. Birkhaüser, Boston, 2002b) for much more.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of MathematicsUniversity Cergy-PontoiseCergy-PontoiseFrance

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