2016/05/04 by Minkyoung Kang, Kang, Minkyoung, Brani Vidaković +1
Chemistry · Computer Science · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Image and Signal Denoising Methods #Methodology (stat.ME) #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.1605.01146
openalex publication_date 2016/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A number of phenomena in various fields such as geology, atmospheric sciences, economics, to list a few, can be modeled as a fractional Brownian motion indexed by Hurst exponent H. This exponent is related to the degree of regularity and self-similarity present in the signal, and it often captures important characteristics useful in various applications. Given its importance, a number of methods have been developed for the estimation of the Hurst exponent. Typically, the proposed methods do not utilize prior information about scaling of a signal. Some signals are known to possess a theoretical value of the Hurst exponent, which motivates us to propose a Bayesian approach that incorporates this information via a suitable elicited prior distribution on H. This significantly improves the accuracy of the estimation, as we demonstrate by simulations. Moreover, the proposed method is robust to small misspecifications of the prior location. The proposed method is applied to a turbulence time series for which Hurst exponent is theoretically known by Kolmogorov's K41 theory.