SOME COMMENTS ON THE CORRELATION DIMENSION OF 1/F-ALPHA NOISE

It has recently been observed by Osborne and Provenzale that a stochastic (infinite degree of freedom) time series with a 1/f-alpha power spectrum can exhibit a finite correlation dimension, even for arbitrarily large data sets. 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 Gausian 1/f-alpha 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.