2007/11/13 by A. Carbone, Anna Carbone · 96 citations
Earth and Planetary Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Cholesky decomposition #Complex Systems and Time Series Analysis #Computer science #Detrended fluctuation analysis #Exponent #Factorization #Filter (signal processing) #Fractal #Geometry #Hurst exponent #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Physics #Statistics #Tree-ring climate responses #Variance (accounting) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.76.056703
published in Physical Review E 76(5), 056703 (American Physical Society)
openalex publication_date 2007/11/13 · arxiv created 2007/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose an algorithm to estimate the Hurst exponent of high-dimensional fractals, based on a generalized high-dimensional variance around a moving average low-pass filter. As working examples, we consider rough surfaces generated by the random midpoint displacement and by the Cholesky-Levinson factorization algorithms. The surrogate surfaces have Hurst exponents ranging from 0.1 to 0.9 with step 0.1, and different sizes. The computational efficiency and the accuracy of the algorithm are also discussed.