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On defining long-range dependence

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde  and
Y. Yang
C. C. Heyde*
Affiliation:
Australian National University and Columbia University
Y. Yang*
Affiliation:
Columbia University
*
∗Postal address: Stochastic Analysis Group, School of Mathematical Sciences, The Australian National University, Canberra, ACT 0200, Australia and Department of Statistics, Columbia University, New York, NY 10027, USA.
∗∗Postal address: Department of Statistics, Columbia University, New York, NY 10027, USA.
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Abstract

Long-range dependence has usually been defined in terms of covariance properties relevant only to second-order stationary processes. Here we provide new definitions, almost equivalent to the original ones in that domain of applicability, which are useful for processes which may not be second-order stationary, or indeed have infinite variances. The ready applicability of this formulation for categorizing the behaviour for various infinite variance models is shown.

Keywords

LONG-RANGE DEPENDENCEPERSISTENCEFRACTAL MODELSALLEN VARIANCEINFINITE VARIANCE MODELSFRACTIONAL STABLE NOISE

MSC classification

Primary: 60G10: Stationary processes 60G18: Self-similar processes
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 4 , December 1997 , pp. 939 - 944
Copyright
Copyright © Applied Probability Trust 1997 

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