Bayesian estimation of the self-similarity exponent of the Nile River fluctuation
- 1Departement of Mathematics, University of Bourdj-Bouarreridj, Box 64, 34265 Bourdj-Bouarreridj, Algeria
- 2Institute for Mathematics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany
- 3Departement of Mathematics, University of M'Sila, Box 166, Msila, Algeria
Abstract. The aim of this paper is to estimate the Hurst parameter of Fractional Gaussian Noise (FGN) using Bayesian inference. We propose an estimation technique that takes into account the full correlation structure of this process. Instead of using the integrated time series and then applying an estimator for its Hurst exponent, we propose to use the noise signal directly. As an application we analyze the time series of the Nile River, where we find a posterior distribution which is compatible with previous findings. In addition, our technique provides natural error bars for the Hurst exponent.