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Power-law correlations, related models for long-range dependence and their simulation

Part of: Harmonic analysis in one variable Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Tilmann Gneiting
Tilmann Gneiting*
Affiliation:
University of Washington
*
∗ Postal address: Department of Statistics, Box 354322, University of Washington, Seattle, Washington 98195-4322, USA.
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Abstract

Martin and Walker ((1997) J. Appl. Prob.34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward proof of their conjecture on the permissible range of c is given, and various other models for long-range dependence are discussed. In particular, the Cauchy family ρ(v) = (1 + |v/c|α)-β/α allows for the simultaneous fitting of both the long-term and short-term correlation structure within a simple analytical model. The note closes with hints at the fast and exact simulation of fractional Gaussian noise and related processes.

Keywords

Cauchy familycorrelation functionfractional noiselong-memorypower-lawsimulationtime series

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) 60G10: Stationary processes 60G18: Self-similar processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1104 - 1109
Copyright
Copyright © by the Applied Probability Trust 2000 

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