Using the method of Akaike's Information Criterion (AIC), we present a critical discussion on the determination of the order (i.e., “memory”) of an ergodic Markov chain with a finite number of states. We apply this method to sequences of wet and dry days observed at Manchester and Liverpool, England. We reexamine the Tel Aviv data and argue that a Markov chain of order not lower than 2 should be fitted, instead of the previously fitted first order. We further consider the use of AIC in investigating local stationarity. Finally, the sensitivity of the method when the sample size is reduced is briefly examined. The method proposed in this paper will enable practicing meteorologists to set up an automatic “Markov chain modeler”.