Article2005

Identification of multifractional Brownian motion

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

Abstract

We develop a method for estimating the Hurst function of a multifractional Brownian motion, which is an extension of the fractional Brownian motion in the sense that the path regularity can now vary with time. This method is based on a local estimation of the second-order moment of a unique discretized filtered path. The effectiveness of our procedure is investigated in a short simulation study.

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References

1968Fractional Brownian Motions, Fractional Noises and Applications 1983THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS 1996Statistics for Long-Memory Processes.1975Weak convergence to fractional brownian motion and to the rosenblatt process 1997Quadratic variations and estimation of the local Hölder index of a Gaussian process 2001Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths 1998Identifying the multifractional function of a Gaussian process

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2011Modeling stock prices by multifractional Brownian motion: an improved estimation of the pointwise regularity 2011Measuring the roughness of random paths by increment ratios 2012Nonparametric estimation of the local Hurst function of multifractional Gaussian processes 2022Forecasting with fractional Brownian motion: a financial perspective 2014Asymptotic behavior of mixed power variations and statistical estimation in mixed models

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