Power-law correlations, related models for long-range dependence and their simulation
- 1 December 2000
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 37 (4) , 1104-1109
- https://doi.org/10.1239/jap/1014843088
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
This publication has 13 references indexed in Scilit:
- Analyzing exact fractal time series: evaluating dispersional analysis and rescaled range methodsPhysica A: Statistical Mechanics and its Applications, 1997
- A power-law model and other models for long-range dependenceJournal of Applied Probability, 1997
- Fast and Exact Simulation of Stationary Gaussian Processes through Circulant Embedding of the Covariance MatrixSIAM Journal on Scientific Computing, 1997
- Statistical Methods for Data with Long-Range DependenceStatistical Science, 1992
- Tests for Hurst effectBiometrika, 1987
- Fractional differencingBiometrika, 1981
- AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCINGJournal of Time Series Analysis, 1980
- A Fast Fractional Gaussian Noise GeneratorWater Resources Research, 1971
- On the reduction (mod 1) of completely monotone functions (0, ∞)Annali di Matematica Pura ed Applicata (1923 -), 1957
- LV. The Bernoullian Fourier diagramsJournal of Computers in Education, 1947