On modes of long-range dependence

Abstract

This 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. Show more