A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary framework
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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 θ. We present an adaptation of the absolute-moment method to this framework and we compare it to the maximum likelihood method, with simulations. The conclusion is mainly in favour of the adapted absolute-moment method for several reasons: it makes it possible to confirm visually that the model is well specified, it is computationally more performing, the estimation of θ is more accurate.
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