Nonstationary Yule-Walker equations

A nonstationary generalization of the classical Yule-Walker equations, relating the (time-varying) autocorrelations of an autoregressive process to the coefficients of the possible models for this process, is given. The corresponding theoretical model-building (or spectral factorization) problem, i.e., that of expressing the above mentioned models in terms of the autocorrelations, is solved. This paper, as well as several others, is part of a work whose purpose is a systematic study of time-varying ARMA models.