Long-range dependence

Long-range dependence (LRD), also called long memory or long-range persistence, is a phenomenon that may arise in the analysis of spatial or time series data. It relates to the rate of decay of statistical dependence of two points with increasing time interval or spatial distance between the points. A phenomenon is usually considered to have long-range dependence if the dependence decays more slowly than an exponential decay, typically a power-like decay. LRD is often related to self-similar processes or fields. LRD has been used in various fields such as internet traffic modelling, econometrics, hydrology, linguistics and the earth sciences. Different mathematical definitions of LRD are used for different contexts and purposes.[1][2][3][4][5][6]

  1. ^ Beran, Jan (1994). Statistics for Long-Memory Processes. CRC Press.
  2. ^ Doukhan; et al. (2003). Theory and Applications of Long-Range Dependence. Birkhäuser.
  3. ^ Malamud, Bruce D.; Turcotte, Donald L. (1999). Self-Affine Time Series: I. Generation and Analyses. Vol. 40. pp. 1–90. Bibcode:1999AdGeo..40....1M. doi:10.1016/S0065-2687(08)60293-9. ISBN 9780120188406. {{cite book}}: |journal= ignored (help)
  4. ^ Samorodnitsky, Gennady (2007). Long range dependence. Foundations and Trends in Stochastic Systems.
  5. ^ Beran; et al. (2013). Long memory processes: probabilistic properties and statistical methods. Springer.
  6. ^ Witt, Annette; Malamud, Bruce D. (September 2013). "Quantification of Long-Range Persistence in Geophysical Time Series: Conventional and Benchmark-Based Improvement Techniques". Surveys in Geophysics. 34 (5): 541–651. Bibcode:2013SGeo...34..541W. doi:10.1007/s10712-012-9217-8.