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When noisy data is subject to Correlation Dimension (d2) estimation, spurious results may arise because noise will produce a d2 value similar to the embedding dimension used. Thus noise will produce a d2 estimate of 3 when the data is embedded in 3 dimensions.

To check for determinism, data points are shuffled. This operation preserves the probability distribution but generally produces a very different power spectrum and correlation function.

Correlation Dimensional estimates are performed at increasing values of embedding dimension. The shuffled data will show a linear relationship. If the original data exhibits determinism, the attractor dimension will tend to a plateau. (See Anesthesiology Web Enhancement Patient M Data versus shuffled data).

* Sprott JC, Rowlands G. Chaos Data Analyzer. The Professional Version. User's Manual. Raleigh NC, Physics Academic Software, 2003, 31-32