Some comments on the correlation dimension of 1/fα noise
Abstract
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, Physica D 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 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: Phys. Lett. A 155 (1991) 480--493.
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