Journal of Applied Probability

On modes of long-range dependence

C. C. Heyde

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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.

Article information

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

Dates
First available in Project Euclid: 20 November 2002

Permanent link to this document
http://projecteuclid.org/euclid.jap/1037816026

Digital Object Identifier
doi:10.1239/jap/1037816026

Mathematical Reviews number (MathSciNet)
MR1938178

Zentralblatt MATH identifier
1016.60040

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

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

Citation

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


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