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

Strictly stationary solutions of multivariate ARMA equations with i.i.d. noise