{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T17:14:16Z","timestamp":1776273256011,"version":"3.50.1"},"reference-count":88,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T00:00:00Z","timestamp":1503446400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here, we discuss the original motivation of the development of long memory and Mandelbrot\u2019s influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities.<\/jats:p>","DOI":"10.3390\/e19090437","type":"journal-article","created":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T11:32:27Z","timestamp":1503487947000},"page":"437","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":123,"title":["A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951\u20131980"],"prefix":"10.3390","volume":"19","author":[{"given":"Timothy","family":"Graves","sequence":"first","affiliation":[{"name":"Statistics Laboratory, University of Cambridge, Cambridge CB3 0WB, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Gramacy","sequence":"additional","affiliation":[{"name":"Statistics Laboratory, University of Cambridge, Cambridge CB3 0WB, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4484-6588","authenticated-orcid":false,"given":"Nicholas","family":"Watkins","sequence":"additional","affiliation":[{"name":"Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry CV4 7AL, UK"},{"name":"Centre for the Analysis of Time Series, London School of Economics and Political Sciences, London WC2A 2AE, UK"},{"name":"Faculty of Science, Technology, Engineering and Mathematics, Open University, Milton Keynes MK7 6AA, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Franzke","sequence":"additional","affiliation":[{"name":"Meteorological Institute, Center for Earth System Research and Sustainability, University of Hamburg, 20146 Hamburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,23]]},"reference":[{"key":"ref_1","unstructured":"Beran, J. 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