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

TR Number
Date
2017-08-23
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI
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.

Description
Keywords
long-range dependence, Hurst effect, fractionally differenced models, Mandelbrot
Citation
Entropy 19 (9): 437 (2017)