On modes of long-range dependence

C. C. Heyde*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    22 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)882-888
    Number of pages7
    JournalJournal of Applied Probability
    Volume39
    Issue number4
    DOIs
    Publication statusPublished - Dec 2002

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