| Non-stationary Markov chains have received very little attention in the literature. We consider chains where the n-step transition probabilities are periodic in n. Such chains occur in genetics. A gene can be modeled as a k-step Markov chain with transition probabilities that have 3-periodicity. We consider the problem: given a realization of a (finite state space) stochastic process to classify it as arising from a Markov chain with periodic transition probabilities with a period p or from a Markov chain with stationary transition probabilities. We propose a statistic and illustrate its efficacy via simulation results. |