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The paper established sufficient conditions of predictability with degeneracyfor the spectrum at $M$-periodically located isolated points on the unitcircle. It is also shown that $m$-periodic subsequences of these sequences arealso predictable if $m$ is a divisor of $M$. The predictability can be achievedfor finite horizon with linear predictors defined by convolutions with certainkernels. As an example of applications, it is shown that there exists a classof sequences that is everywhere dense in the class of all square-summablesequences and such that its members can be recovered from their periodicsubsequences. This recoverability is associated with certain spectrumdegeneracy of a new kind.

Predictability of sequences and subsequences with spectrum degeneracy at periodically located points