Journal of Applied Probability

On modes of long-range dependence

C. C. Heyde

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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.

Article information

J. Appl. Probab. Volume 39, Number 4 (2002), 882-888.

First available in Project Euclid: 20 November 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G10: Stationary processes 91B70: Stochastic models
Secondary: 60G18: Self-similar processes 60G15: Gaussian processes

Long-range dependence persistence of signs persistence of magnitudes fractional Brownian motion risky asset models FATGBM model multifractal model


Heyde, C. C. On modes of long-range dependence. J. Appl. Probab. 39 (2002), no. 4, 882--888. doi:10.1239/jap/1037816026.

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