  The paper suggests a method of recovering missing values for sequences,
including sequences with a multidimensional index, based on optimal
approximation by processes featuring spectrum degeneracy. The problem is
considered in the pathwise setting, without using probabilistic assumptions on
the ensemble. The method requires to solve a closed linear equation connecting
the available observations of the underlying process with the values of the
approximating process with degenerate spectrum outside the observation
range.Some robustness with respect to noise contamination is established for
the suggested recovering algorithm. It is suggested to apply this data recovery
algorithm to forecasting with a preselected dummy long-horizon forecast that
helps to regularize the solution.
