@article{MakaravaBenmehdiHolschneider2011,
  author    = {Makarava, Natallia and Benmehdi, Sabah and Holschneider, Matthias},
  title     = {Bayesian estimation of self-similarity exponent},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {84},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.84.021109},
  pages     = {9},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}
@article{BenmehdiMakaravaBenhamidoucheetal.2011,
  author    = {Benmehdi, Sabah and Makarava, Natallia and Benhamidouche, N. and Holschneider, Matthias},
  title     = {Bayesian estimation of the self-similarity exponent of the Nile River fluctuation},
  series = {Nonlinear processes in geophysics},
  volume    = {18},
  journal   = {Nonlinear processes in geophysics},
  number    = {3},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1023-5809},
  doi       = {10.5194/npg-18-441-2011},
  pages     = {441 -- 446},
  year      = {2011},
  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.},
  language  = {en}
}