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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., Comment: 14 pages, compressed and uuencoded postscript file, figures included. Also available by anonymous ftp at ftp://ftp.santafe.edu/pub/mp/epr

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.