Methodol Comput Appl Probab (2017) 19:973–983
Bayesian Approach to Hurst Exponent Estimation
· Jaromir Kukal
· Oldrich Vysata
Received: 31 October 2015 / Revised: 19 August 2016 /
Accepted: 9 January 2017 / Published online: 18 January 2017
© Springer Science+Business Media New York 2017
Abstract Fractal investigation of a signal often involves estimating its fractal dimension or
Hurst exponent H when considered as a sample of a fractional process. Fractional Gaussian
noise (fGn) belongs to the family of self-similar fractional processes and it is dependent
on parameter H . There are variety of traditional methods for Hurst exponent estimation.
Our novel approach is based on zero-crossing principle and signal segmentation. Thanks to
the Bayesian analysis, we present a new axiomatically based procedure of determining the
expected value of Hurst exponent together with its standard deviation and credible intervals.
The statistical characteristics are calculated at the interval level at first and then they are
used for the deduction of the aggregate estimate. The methodology is subsequently used for
the EEG signal analysis of patients suffering from Alzheimer disease.
Keywords Fractal dimension · Hurst exponent · Bayesian approach · EEG · Alzheimer
Mathematics Subject Classification (2010) 60G15 · 62C10
FNSPE CTU, Trojanova 13, 120 00, Praha 2, Czech Republic
Faculty of Medicine in Hradec Kralove, Charles University, Simkova 870, 500 38, Hradec Kralove,