The partial realization problem for moving average models

The author considers the problem of finding the minimum-order moving average (MA) model which jointly matches a set of correlation, power spectral, and/or impulse response values. He provides a solution for the case when correlations alone, or correlations and spectral values are specified. The solution rests on a representation of the set of attainable correlation/spectral values which a given order MA model can produce in terms of the eigenstructure of certain Toeplitz matrices. When impulse response values are included, the problem complicates because certain key attainable sets become nonconvex. Bounds for this case, involving generalized eigenvalues are provided