Rational q× q Carath\'eodory Functions and Central Non-negative Hermitian Measures
Abstract
We give an explicit representation of central measures corresponding to finite Toeplitz non-negative definite sequences of complex q× q matrices. Such measures are intimately connected to central q× q Carath\'eodory functions. This enables us to prove an explicit representation of the non-stochastic spectral measure of an arbitrary multivariate autoregressive stationary sequence in terms of the covariance sequence.
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