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Entropy 2017, 19(9), 437;

A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951–1980

Statistics Laboratory, University of Cambridge, Cambridge CB3 0WB, UK
Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry CV4 7AL, UK
Centre for the Analysis of Time Series, London School of Economics and Political Sciences, London WC2A 2AE, UK
Faculty of Science, Technology, Engineering and Mathematics, Open University, Milton Keynes MK7 6AA, UK
Meteorological Institute, Center for Earth System Research and Sustainability, University of Hamburg, 20146 Hamburg, Germany
Current address: Arup, London W1T 4BQ, UK.
Current address: Department of Statistics, Virginia Polytechnic and State University, Blacksburg, VA 24061, USA.
Author to whom correspondence should be addressed.
Received: 24 May 2017 / Revised: 3 August 2017 / Accepted: 18 August 2017 / Published: 23 August 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
Full-Text   |   PDF [812 KB, uploaded 23 August 2017]


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’s influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities. View Full-Text
Keywords: long-range dependence; Hurst effect; fractionally differenced models; Mandelbrot long-range dependence; Hurst effect; fractionally differenced models; Mandelbrot
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Graves, T.; Gramacy, R.; Watkins, N.; Franzke, C. A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951–1980. Entropy 2017, 19, 437.

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