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arXiv · 2003.02566

A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary framework

Matthieu Garcin
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Abstract

The absolute-moment method is widespread for estimating the Hurst exponent of a fractional Brownian motion $X$. But this method is biased when applied to a stationary version of $X$, in particular an inverse Lamperti transform of $X$, with a linear time contraction of parameter $\theta$. We present an adaptation of the absolute-moment method to this framework and we compare it to the maximum likelihood method, with simulations and an application to a financial time series. While it appears that the maximum-likelihood method is more accurate than the adapted absolute-moment estimation, this last method is not uninteresting for two reasons: it makes it possible to confirm visually that the model is well specified and it is computationally more performing.

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Matthieu Garcin. 2020-03-05. A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary framework. https://arxiv.org/abs/2003.02566

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