Premium
An Estimate of the Fractal Index Using Multiscale Aggregates
Author(s) -
Poggi JohnMichel,
Viano MarieClaude
Publication year - 1998
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00087
Subject(s) - mathematics , estimator , fractal , fractional brownian motion , gaussian , quadratic equation , statistics , brownian motion , mathematical analysis , gaussian process , statistical physics , geometry , physics , quantum mechanics
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