  The paper suggests a method of extrapolation of notion of one-sided
semi-infinite sequences representing traces of two-sided band-limited
sequences; this features ensure uniqueness of this extrapolation and
possibility to use this for forecasting. This lead to a forecasting method for
more general sequences without this feature based on minimization of the mean
square error between the observed path and a predicable sequence. These
procedure involves calculation of this predictable path; the procedure can be
interpreted as causal smoothing. The corresponding smoothed sequences allow
unique extrapolations to future times that can be interpreted as optimal
forecasts.
