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Generators of long-range dependent processes: A survey

Jean‐Marc Bardet · Georges Oppenheim · Anne Philippe · Murad S. Taqqu

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Complex Systems and Time Series Analysis Stochastic processes and financial applications Fractional Differential Equations Solutions

Abstract

We describe methods for generating discretized sample paths of long-range dependent processes such as fractional Brownian motion, its increment fractional Gaussian noise and FARIMA processes.

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1996Statistics for Long-Memory Processes.1995ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY 1992Maximum likelihood estimation of stationary univariate fractionally integrated time series models 1999Stochastic Analysis of the Fractional Brownian Motion 1987Tests for Hurst Effect 1994Simulation of Stationary Gaussian Processes in [0, 1]d 2008Long Memory Relationships and the Aggregation of Dynamic Models 1998On estimating the intensity of long-range dependence in finite and infinite variance time series

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2008Asymptotic Properties of the Detrended Fluctuation Analysis of Long-Range-Dependent Processes

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