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By determining the delay value, the correlation integrals were computed by the Grassberger-Procaccia algorithm for different embedding dimensions (m) from m = 1 to m = 25 (Figure 4a).
The neural network input dimension equals the embedding dimension m.
For the same time series data, the best embedding dimension obtained by using the Cao method is shown in Figure 5.
Based on the analysis above, the number of input nodes of the neural network is determined as the value of the embedding dimension, i.
The prediction accuracy is relatively high with low embedding dimension factors but not ideal with high embedding dimension factors.
Selection of embedding dimensions generally involves the G-P method of saturated correlation dimension, the false nearest neighbor algorithm and the Cao algorithm.
The program automatically chooses the optimal e and leaves two parameters under user control: the embedding dimension (D) and the parameter (n), which is the number of sample intervals over which each pair of points is followed before a new pair is chosen.
The CD increases with the embedding dimension but does not explode.
The CDs of the residuals of the filtered data in Panels Al and A2 increase with the embedding dimension but do not explode, which is an indication of nonlinearity.
420977 Number of Daily Returns 269,867 243,333 TABLE 2 Correlation Dimensions and the BDS Statistics at Embedding Dimensions 2 Through 10 and n Equaling 1, 2, 4, and 8, for the Daily Raw Returns of Life-Health and Property-Liability Insurance Portfolios Panel A1: Correlation Dimension, Life-Health Insurance Portfoliio Embedding Dimension n 2 3 4 5 6 7 8 9 1 2.
750, n = 2000), daily gold returns, silver returns, and their various components over four embedding dimensions 5, 10, 15, 20.