Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise

Abstract

Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent (H) . Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing the spectral exponent from a linear function to a piecewise polynomial, we obtained a closer approximation of the fGn's spectral density function. This procedure is significant because it reduced the bias in the estimation of H . Furthermore, the averaging technique that we used markedly reduced the variance of estimates. We also considered the asymptotical unbiasedness of the method and derived the upper bound of its variance and confidence interval. Monte Carlo simulations showed that the proposed estimator was superior to a wavelet maximum likelihood estimator in terms of mean-squared error and was comparable to Whittle's estimator. In addition, a real data set of Nile river minima was employed to evaluate the efficiency of our proposed method. These tests confirmed that our proposed method was computationally simpler and faster than Whittle's estimator.