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Identification of the scaling region

To improve the reliability of the identification of a scaling region, Albano et. al [Albano et al., 1987] impose the following series of criteria:
  1. The degree of divergence of the derivative in the scaling region should not exceed 10%;
  2. The scaling region should extend for at least two decades (cf. figure 7.9...);
  3. 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.


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