Spectral factorization of wide sense stationary processes on \({\mathbb{Z}}^ 2\)
To extend the prediction problem from Z to \(Z^ 2\) is not so simple, taking account of the difficulty of extending the nice property of the unit disc to the bidisc and of choosing the past of the processes. In this paper, using an explicit realization of the canonical factorization of the spectral density, the problem of wide sense stationary processes on \(Z^ 2\) with respect to the column-by-column or row-by-row lexicographic order is studied. Also, conditions for a process to have quarter-plane representation in terms of its innovations are given.
canonical factorization of the spectral density
scientific article; zbMATH DE number 3982180
scientific article