  The paper studies recoverability of missing values for sequences in a
pathwise setting without probabilistic assumptions. This setting is oriented on
a situation where the underlying sequence is considered as a sole sequence
rather than a member of an ensemble with known statistical properties.
Sufficient conditions of recoverability are obtained; it is shown that
sequences are recoverable if there is a certain degree of degeneracy of the
Z-transforms. We found that, in some cases, this degree can be measured as the
number of the derivatives of Z-transform vanishing at a point. For processes
with non-degenerate Z-transform, an optimal recovering based on the projection
on a set of recoverable sequences is suggested. Some robustness of the solution
with respect to noise contamination and truncation is established.
