An Estimate of the Fractal Index Using Multiscale Aggregates

We study a family of estimators of the fractal index of a Gaussian process based on the quadratic deviations at different aggregation scales. The estimators are convergent and asymptotically Gaussian when suitably normalized. Confidence intervals are provided. These asymptotic results hold for a large family of stationary-increment models including fractional Brownian motions with square-integrable spectral density. The estimates are applied to the analysis of an electrical signal