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An Estimate of the Fractal Index Using Multiscale Aggregates
Article first published online: 26 DEC 2001
DOI: 10.1111/1467-9892.00087
Blackwell Publishers Ltd 1998
1467-9892/asset/cover.gif?v=1&s=eec782011cf3959dc4aa59555e8f84f3d4459106 "Journal of Time Series Analysis")
Additional Information
How to Cite
Poggi, J.-M. and Viano, M.-C. (1998), An Estimate of the Fractal Index Using Multiscale Aggregates. Journal of Time Series Analysis, 19: 221–233. doi: 10.1111/1467-9892.00087
Publication History
- Issue published online: 26 DEC 2001
- Article first published online: 26 DEC 2001
- First version received
- Abstract
- Cited By
Keywords:
- Confidence interval;
- estimation of fractal index;
- fractional Brownian motion;
- long and intermediate memory;
- self-similarity
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