SPECTRAL FACTORIZATION OF PERIODICALLY CORRELATED MA(1) PROCESSES

The spectral factorization problem, i.e. the problem of obtaining all possible MA representations of a process with given autocovariance fun ction, is considered for univariate, d-periodic MA(1) (equivalently, 1 -dependent in the second-order sense) processes. The solutions are pro vided explicitly, and their invertibility properties are investigated. A characterization, in terms of their autocovariance functions, of no n-invertible d-periodic 1-dependent processes, extending to the period ic case the traditional unit root condition, is provided.