Up: PRACTICAL ASPECTS
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To improve the reliability of the identification of a scaling region,
Albano et. al [Albano et al., 1987] impose the following series
- The degree of divergence of the derivative in the scaling region
should not exceed 10%;
- The scaling region should extend for at least two
decades (cf. figure 7.9...);
- The values of the estimated dimension should be stable within 10%
for at least four consecutive values of the embedding dimension.
The scaling region is usually identified by looking for a straight
region of the correlation integral or a constant region of its
derivative by the naked eye. A method due to Ellner [Ellner, 1988]
can be useful to reduce distorsions of the correlation integral
due to statistical fluctuations at the small distances region so
that the scaling region identified may become longer.