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We give an explicit representation of central measures corresponding tofinite Toeplitz non-negative definite sequences of complex $q\times q$matrices. Such measures are intimately connected to central $q\times q$Carath\'eodory functions. This enables us to prove an explicit representationof the non-stochastic spectral measure of an arbitrary multivariateautoregressive stationary sequence in terms of the covariance sequence.

Rational $q\times q$ Carath\'eodory Functions and Central Non-negative Hermitian Measures