  We consider the problem of designing almost optimal predictors for dynamical
systems from a finite sequence of noisy observations and incomplete knowledge
of the dynamics and the noise. We first discuss the properties of the optimal
(Bayes) predictor and present the limitations of memory-free forecasting
methods, and of any finite memory methods in general. We then show that a
nonparametric support vector machine approach to forecasting can consistently
learn the optimal predictor for all pairs of dynamical systems and bounded
observational noise processes that possess summable correlation sequences.
Numerical experiments show that this approach adapts the memory length of the
forecaster to the complexity of the learning task and the size of the
observation sequence.
