Abstract
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of multivariate ARMA equations with independent and identi- cally distributed driving noise. For general ARMA( p, q) equations these conditions are expressed in terms of the coefficient polynomials of the defining equations and moments of the driving noise sequence, while for p = 1 an additional characteriza- tion 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.
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