Heyde, C C2015-12-132015-12-130021-9002http://hdl.handle.net/1885/92580This paper aims at enhancing the understanding of long-range dependence (LRD) by focusing on mechanisms for generating this dependence, namely persistence of signs and/or persistence of magnitudes beyond what can be expected under weak dependence. These concepts are illustrated through a discussion of fractional Brownian noise of index H ε (0, 1) and it is shown that LRD in signs holds if and only if 1/2 < H < 1 and LRD in magnitudes if and only if 3/4 < H < 1. An application to discrimination between two risky asset finance models, the FATGBM model of Heyde and the multifractal model of Mandelbrot, is given to illustrate the use of the ideas.Keywords: FATGBM model; Fractional Brownian motion; Long-range dependence; Multifractal model; Persistence of magnitudes; Persistence of signs; Risky asset models200210.1239/jap/10378160262015-12-12