Permutation Excess Entropy and Mutual Information between the Past and Future
arXiv:1112.2491
Abstract
We address the excess entropy, which is a measure of complexity for stationary time series, from the ordinal point of view. We show that the permutation excess entropy is equal to the mutual information between two adjacent semi-infinite blocks in the space of orderings for finite-state stationary ergodic Markov processes. This result may shed a new light on the relationship between complexity and anticipation.
14 pages, 10th International Conference on Computing Anticipatory Systems, Liege, Belgium, August 11, 2011