Mutual information, strange attractors, and the optimal estimation of dimension

It has been shown that the appropriate setting of data windows is crucial to a successful estimation of a time-series correlation dimension using the Grassberger-Procaccia algorithm [Physica 9D, 189 (1983); Phys. Rev. Lett. 50, 346 (1983)], and it has been proposed that the first minimum of the corresponding mutual-information function may be an appropriate window value. We have tested this hypothesis against data generated by the Rössler equations, the Lorenz equations, and a three-dimensional irrational torus. We conclude that mutual information is not consistently successful in identifying the optimal window.