A note on Bayesian wavelet-based estimation of scaling

Abstract

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.

References in corpus (4)

• Anisotropic scaling of magnetohydrodynamic turbulence
• Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case $H=1/4$
• Modeling turbulent wave-front phase as a fractional Brownian motion: a new approach
• On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion

Cited by in corpus (1)

• Fractional Gaussian noise: Prior specification and model comparison