A Simple and Effective Algorithm to Calculate the Hurst Exponent

Abstract

In 1951 the British hydrologist Harold Edwin Hurst published the paper: “Long Term Storage Capacity of
Reservoirs”. The paper introduced the Hurst Exponent. It was a tool to analyze river flows to help determine the
appropriate size of a reservoir. In 1968 Benoit B. Mandelbrot and John Van Ness published the seminal paper
“Fractional Brownian Motions, Fractional Noises and Applications” In effect this paper broadened the
applications of the Hurst Exponent to time series in physics, geophysical sciences, medical science, biology,
information sciences, economics, finance, etc. The present paper presents an algorithm to calculate the Hurst
Exponent. It is based on the “bootstrap method” introduced by Bradley Efron in 1979. It is simple to implement,
and permits the assignment of measures of accuracy to the estimand.