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The paper suggests a method of extrapolation of notion of one-sidedsemi-infinite sequences representing traces of two-sided band-limitedsequences; this features ensure uniqueness of this extrapolation andpossibility to use this for forecasting. This lead to a forecasting method formore general sequences without this feature based on minimization of the meansquare error between the observed path and a predicable sequence. Theseprocedure involves calculation of this predictable path; the procedure can beinterpreted as causal smoothing. The corresponding smoothed sequences allowunique extrapolations to future times that can be interpreted as optimalforecasts.

On causal extrapolation of sequences with applications to forecasting