  We obtain necessary and sufficient conditions for the existence of strictly
stationary solutions of multivariate ARMA equations with independent and
identically distributed noise. For general ARMA$(p,q)$ equations these
conditions are expressed in terms of the characteristic polynomials of the
defining equations and moments of the driving noise sequence, while for $p=1$
an additional characterization is obtained in terms of the Jordan canonical
decomposition of the autoregressive matrix, the moving average coefficient
matrices and the noise sequence. No a priori assumptions are made on either the
driving noise sequence or the coefficient matrices.
