  Based on information theory, we present a method to determine an optimal
Markov approximation for modelling and prediction from time series data. The
method finds a balance between minimal modelling errors by taking as much as
possible memory into account and minimal statistical errors by working in
embedding spaces of rather small dimension. A key ingredient is an estimate of
the statistical error of entropy estimates. The method is illustrated with
several examples and the consequences for prediction are evaluated by means of
the root mean squard prediction error for point prediction.
