Resumen
In this paper, we give a characterization of the range of spectral matrices, which are feasible for bivariate VAR(p) models. In addition to the marginal spectra and the cross-spectrum being ratios of trigonometric polynomials, as is also the case for VARMA(p,q) models, in the VAR(p) case the polynomials involved as numerators and denominators must fulfil further restrictions. We state these restrictions and we show that they are also sufficient for a spectral matrix to belong to a VAR. We demonstrate how these polynomials may be regained only from the marginal spectra and the coherency. This, in turn, is used to construct a visual goodness-of-fit criterion for fitting a VAR model, yielding also indications on the necessary order. The feasible phase lags between frequency-@l-components of the two series are discussed in detail. Finally, we propose two methods for constructing VAR models with (partially) pre-specified spectral elements. Examples are provided illustrating the criterion, the phase-lag structure and the above methods.