1993/02/10 by James Theiler, Theiler, James
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Fractal and DNA sequence analysis #Statistical Mechanics and Entropy #comp-gas #nlin.CG
paper · pdf · doi:10.48550/arxiv.comp-gas/9302001
CYCLER Paper 93feb005 Several PostScript files, compress'ed tar'ed uuencode'ed
arxiv created 1993/02/10 · openalex publication_date 1993/02/10 · arxiv updated 2009/11/30 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
It has recently been observed that a stochastic (infinite degree of freedom) time series with a 1/fα power spectrum can exhibit a finite correlation dimension, even for arbitrarily large data sets. [A.R. Osborne and A.~Provenzale, \sl Physica D \bf 35, 357 (1989).] I will discuss the relevance of this observation to the practical estimation of dimension from a time series, and in particular I will argue that a good dimension algorithm need not be trapped by this anomalous fractal scaling. Further, I will analytically treat the case of gaussian \onefas noise, with explicit high and low frequency cutoffs, and derive the scaling of the correlation integral C(N,r) in various regimes of the (N,r) plane. Appears in: \sl Phys. Lett. A \bf 155 (1991) 480--493.