Preprint Review Version 1 This version is not peer-reviewed

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

Version 1 : Received: 26 May 2017 / Approved: 26 May 2017 / Online: 26 May 2017 (18:36:50 CEST)

A peer-reviewed article of this Preprint also exists.

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. 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.

Journal reference: Entropy 2017, 19, 437
DOI: 10.3390/e19090437

Abstract

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

Subject Areas

long-range dependence; Hurst effect; fractionallydifferenced models; Mandelbrot

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