Fractal estimation using models on multiscale trees

We estimate the Hurst parameter H of fractional Brownian motion (or, by extension, the fractal exponent φ of stochastic processes having 1/f^φ-like spectra) by applying a multiresolution framework. This framework admits an efficient likelihood function evaluation, allowing us to compute the maximum likelihood estimate of this fractal parameter with relative ease. In addition to yielding results that compare well with other proposed methods, and in contrast with other approaches, our method is directly applicable with, at most, very simple modification in a variety of other contexts including fractal estimation given irregularly sampled data or nonstationary measurement noise and the estimation of fractal parameters for 2-D random fields