Stability conditions for the time-varying linear predictor

The stability of the inverse of the optimum forward prediction error filter obtained when the input data is nonstationary is investigated. Due to this nonstationary character, the resulting system (which is obtained assuming optimality on a sample-by-sample basis) is time-varying. It turns out that an extension of the Levinson recursion still provides a means to order-update the prediction error filters, leading to asymmetric lattice realizations of the filters. Sufficient conditions on the input process are given in order to ensure exponential asymptotic stability of the corresponding inverse system. Thus this work extends the well-known result from linear prediction theory which states that the transfer function of the optimum forward prediction error filter for a stationary process is minimum phase.