TY  - JOUR
A1  - Makarava, Natallia
A1  - Benmehdi, Sabah
A1  - Holschneider, Matthias
T1  - Bayesian estimation of self-similarity exponent
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.
Y1  - 2011
U6  - https://doi.org/10.1103/PhysRevE.84.021109
SN  - 1539-3755
VL  - 84
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Benmehdi, Sabah
A1  - Makarava, Natallia
A1  - Benhamidouche, N.
A1  - Holschneider, Matthias
T1  - Bayesian estimation of the self-similarity exponent of the Nile River fluctuation
JF  - Nonlinear processes in geophysics
N2  - 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.
Y1  - 2011
U6  - https://doi.org/10.5194/npg-18-441-2011
SN  - 1023-5809
VL  - 18
IS  - 3
SP  - 441
EP  - 446
PB  - Copernicus
CY  - Göttingen
ER  -