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

Published online by Cambridge University Press:  14 July 2016

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

Abstract

Martin and Walker ((1997) J. Appl. Prob.34, 657–670) proposed the power-law ρ(v) = c|v|, |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.

Type
Short Communications
Copyright
Copyright © by the Applied Probability Trust 2000 

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