  Current methods for determining whether a time series exhibits fractal
structure (FS) rely on subjective assessments on estimators of the Hurst
exponent (H). Here, I introduce the Bayesian Assessment of Scaling, an
analytical framework for drawing objective and accurate inferences on the FS of
time series. The technique exploits the scaling property of the diffusion
associated to a time series. The resulting criterion is simple to compute and
represents an accurate characterization of the evidence supporting different
hypotheses on the scaling regime of a time series. Additionally, a closed-form
Maximum Likelihood estimator of H is derived from the criterion, and this
estimator outperforms the best available estimators.
