Long-range dependenceLong-range dependence (LRD), also called long memory or long-range persistence, is a phenomenon that may arise in the analysis of spatial or time series data. It relates to the rate of decay of statistical dependence of two points with increasing time interval or spatial distance between the points. A phenomenon is usually considered to have long-range dependence if the dependence decays more slowly than an exponential decay, typically a power-like decay. LRD is often related to self-similar processes or fields.
Fractional Brownian motionIn probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process on , that starts at zero, has expectation zero for all in , and has the following covariance function: where H is a real number in (0, 1), called the Hurst index or Hurst parameter associated with the fractional Brownian motion.
