Permutation Excess Entropy and Mutual Information between the Past and   Future
  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. 
Taichi Haruna and Kohei Nakajima
nlin.CD cs.IT math.IT physics.data-an