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We present a new method for nonlinear prediction of discrete random sequencesunder minimal structural assumptions. We give a mathematical construction foroptimal predictors of such processes, in the form of hidden Markov models. Wethen describe an algorithm, CSSR (Causal-State Splitting Reconstruction), whichapproximates the ideal predictor from data. We discuss the reliability of CSSR,its data requirements, and its performance in simulations. Finally, we compareour approach to existing methods using variablelength Markov models andcross-validated hidden Markov models, and show theoretically and experimentallythat our method delivers results superior to the former and at least comparableto the latter.

Blind Construction of Optimal Nonlinear Recursive Predictors for Discrete Sequences