The analysis developed by H.E. Hurst to determine long-memory effects and fractional Brownian motion. Rescaled range analysis measures how the distance covered by a particle increases as we look at longer and longer time scales. For Brownian motion, the distance covered increases with the square root of time. A series which increases at a different rate is not random. See: Anti-persistence, Fractional Brownian Motion, Hurst Exponent, Persistence, Joseph Effect, Noah Effect.