PERIODIC ARMA MODELS: OPTIMAL PREDICTION AND MINIMUM-PHASE CONDITION

The main objective of this paper is to supply the solution of the prediction problem for ARMA models with periodic coefficients (PARMA models). The basic tool is Kaiman prediction theory applied to a suitable state-space representation of the given model. Among other things, the notion of minimum-phase PARMA is introduced. It is shown that the prediction rule for minimum-phase PARMA's can be given a simple input/output form which generalizes the well known time-invariant ARMA predition formula. In the nonminimum-phase case, the solution of the prediction problem call for a suitable notion of canonical representation of the cyclostationary process associated with the original PARMA.