A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA

TL;DR

This paper reviews the historical development of long memory theory, highlighting Mandelbrot's influence and contrasting approaches across scientific disciplines, emphasizing its importance in modeling complex systems.

Contribution

It provides a historical overview of long memory research, focusing on Mandelbrot's role and the diverse perspectives across fields.

Findings

Mandelbrot significantly influenced long memory theory.

Different scientific communities have contrasting approaches to long memory.

Understanding long memory is crucial for modeling complex systems.

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