On recovering missing values in a pathwise setting

The paper suggests sufficient conditions of error-free recoverability of a missing value for sequences, i.e., discrete time processes, in the pathwise setting, without using probabilistic assumptions on the ensemble. This setting targets situations where we deal with a single sequence that is deemed to be unique and such that we cannot rely on statistics collected from other similar samples. A missing value has to be recovered using the intrinsic properties of this single sequence and the observed values. In the paper, error-free recoverability is established for classes of sequences with Z-transform vanishing at a point with a rate that can be chosen arbitrarily. The corresponding recovering kernels are obtained explicitly. Some robustness with respect to noise contamination is established for the suggested recovering algorithm.