  The paper suggests a method of optimal extension of one-sided semi-infinite
sequences of a general type by traces of band-limited sequences in
deterministic setting, i.e. without probabilistic assumptions. The method
requires to solve a closed linear equation in the time domain connecting the
past observations of the underlying process with the future values of the
band-limited process.
  Robustness of the solution with respect to the input errors and data
truncation is established in the framework of Tikhonov regularization.
