Some Further Comments
نویسنده
چکیده
It has recently been observed that a stochastic (in nite degree of freedom) time series with a 1=f power spectrum can exhibit a nite 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 1=f noise, with explicit high and low frequency cuto s, and derive the scaling of the correlation integral C(N; r) in various regimes of the (N; r) plane.
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