When m continues to increase, the limit value of v is the correlation dimension
of the system.
2) By calculating the correlation dimension
d, the embedding dimension m can be determined according to the formula m [greater than or equal to] 2d + 1.
Chaotic features such as Lyapunov exponent, correlation integral, and correlation dimension
are computed and combined with a feature vector.
We deploy two tests of chaos: (i) the Correlation Dimension
of Grassberger and Procaccia (1983) and Takens (1984), (ii) and the BDS statistic of Brock, Dechert, and Scheinkman (1987) which are discussed in detail in Adrangi et al.
In the latter situation, the correlation exponents reach a saturation value, which provides the correlation dimension
of the system.
Distance-based fractal measure is the correlation dimension
In fact, the correlation dimension
belongs to an infinite family of fractal dimensions, as shown for the first time in .
By analysing the correlation dimension
(method of Grassberger & Procaccia, 1983) the author found that in five of the six series analysed (the exception being one of the pairs in the experimental study) the decision-making processes showed chaotic dynamics.
2] ([micro]) is the correlation dimension
of the measure [micro] (see Sect.
Also it is possible to obtain the correlation dimension
because the dimension of each mode converges to a constant value.
For each of these four variables the correlation dimension
Tests based on the correlation dimension
partially confirm the presence of nonlinearity.