  A method for estimating theoretical predictability of time series is
presented, based on information-theoretic functionals---redundancies and
surrogate data technique. The redundancy, designed for a chosen model and a
prediction horizon, evaluates amount of information between a model input
(e.g., lagged versions of the series) and a model output (i.e., a series lagged
by the prediction horizon from the model input) in number of bits. This value,
however, is influenced by a method and precision of redundancy estimation and
therefore it is a) normalized by maximum possible redundancy (given by the
precision used), and b) compared to the redundancies obtained from two types of
the surrogate data in order to obtain reliable classification of a series as
either unpredictable or predictable. The type of predictability (linear or
nonlinear) and its level can be further evaluated. The method is demonstrated
using a numerically generated time series as well as high-frequency foreign
exchange data and the theoretical predictability is compared to performance of
a nonlinear predictor.
