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On modes of long-range dependence

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
C. C. Heyde*
Affiliation:
Australian National University and Columbia University
*
∗ Postal address: Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia. Email address: chris@maths.anu.edu.au
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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 ∈ (0,1) and it is shown that LRD in signs holds if and only if ½ < H < 1 and LRD in magnitudes if and only if ¾ ≤ 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

Long-range dependencepersistence of signspersistence of magnitudesfractional Brownian motionrisky asset modelsFATGBM modelmultifractal model

MSC classification

Primary: 60G10: Stationary processes 91B70: Stochastic models
Secondary: 60G18: Self-similar processes 60G15: Gaussian processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 882 - 888
Copyright
Copyright © Applied Probability Trust 2002 

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