Some comments on the correlation dimension of $1/f^α$ noise
| dc.creator | Theiler, James | |
| dc.date | 1993-02-10 | |
| dc.date.accessioned | 2026-07-07T09:11:00Z | |
| dc.date.available | 2026-07-07T09:11:00Z | |
| dc.description | It has recently been observed that a stochastic (infinite degree of freedom) time series with a $1/f^α$ 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. | |
| dc.description | CYCLER Paper 93feb005 Several PostScript files, compress'ed tar'ed uuencode'ed | |
| dc.identifier | https://arxiv.org/abs/comp-gas/9302001 | |
| dc.identifier | http://arxiv.org/abs/comp-gas/9302001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/151531 | |
| dc.subject | Cellular Automata and Lattice Gases | |
| dc.title | Some comments on the correlation dimension of $1/f^α$ noise | |
| dc.type | text |