A brief history of long memory

Long memory plays an important role, determining the behaviour and predictibility of systems, in many fields; 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 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 contrasting approaches to long memory in the physics and statistics communities with an eye towards their influence on modern practice in these fields.