Prediction of a stationary signal with missing observations

The problem of predicting a discrete-time stationary signal whose past is altered by some missing observations with arbitrary pattern is investigated. The autoregressive (AR) representation of the optimal linear mean-square predictor is obtained under the classical sufficient conditions of existence of such a representation for the predictor based on the complete past. These conditions hold for instance for an ARMA signal. The calculation of the AR representation requires to invert a matrix whose dimension depends on the number of missing values but is independent of their pattern, and whose elements depend only on the AR parameters of the signal. Some properties of the AR representation of the predictor for a finite order AR signal are derived