Universal, nonlinear, mean-square prediction of Markov processes

We estimate the best, nonlinear, mean-square predictor for a Markov process from an observed, finite realization of the process when the true Markov order is unknown. In particular, we propose an universal minimum complexity estimator, which does not know the true Markov order, and yet delivers the same statistical performance as that delivered by a minimum complexity estimator, which knows the true Markov order.