General results on the McMillan degree and the Kronecker indices of ARMA and MFD models

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Abstract
This paper shows that the McMillan degree of general ARMA and MFD models is equal to the pole-zero excess of the matrix consisting of the polynomial factors. Furthermore, the left Kronecker indices are equal to the row degrees of this matrix if and only if it is row-reduced and irreducible. For left coprime ARMA and MFD models the McMillan degree and the left Kronecker indices are related to the determinantal degree and the row degrees of a suitable submatrix of the polynomial factors. Under certain (necessary and sufficient) conditions this information can even be inferred from the denominator matrices in the ARMA and MFD models. Finally a rank test is presented for actually computing the McMillan degree of left coprime ARMA and MFD models.

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