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EMBDSYMPLEC: MATLAB function to determine embedding dimension based on symplectic geometry

Author

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  • Shapour Mohammadi

    () (University of Tehran)

Abstract

Determination of embedding dimension based on symplectic geometry. Let X be lag matrix of y, A=X'X, and A(n) is (n-1) times transformed form of A by Householder matrix. If descending sorted eigenvalues A(n) tend to be constant for dimension d+1 then d is the proper embedding dimension. let sigma be square of eigenvalues of A matrix, sigma1=(lambda^2)max,÷,sigman=(lambda^2)min,where n is the dimension of X. If sigma1>sigma2>÷>sigmad>sigma(d+1)>=...>=sigman, then d is the embedding dimension of the reconstruction system(Lei et al. 2002). The dimension before horizontal section of log(sigmai/tr(sigmai))plot is the proper dimension.

Suggested Citation

  • Shapour Mohammadi, 2009. "EMBDSYMPLEC: MATLAB function to determine embedding dimension based on symplectic geometry," Statistical Software Components T7415011, Boston College Department of Economics.
  • Handle: RePEc:boc:bocode:t741511
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