Abstract
The aim of this paper is to provide simple models with a time-varying Hurst index. Such models should be simple as much as possible and well fit the estimated Hurst index. After a recall on the fractional and multifractional Brownian motion and on the statistical estimation of the Hurst index, we propose a fitting test for a model with a time-varying Hurst index. Then, we give an approach to select a simple model. Our approach is illustrated by numerous numerical simulations and then applied to market finance data.
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