All-pass matrices, the positive real lemma, and unit canonical correlations between future and past

Michael Green

Journal of Multivariate Analysis, 1988, vol. 24, issue 1, 143-154

Abstract: Stationary vector ARMA processess x(t), t = 0, ±1, ±2,..., that are full rank are considered. It is shown, with E(z) denoting the 'symbol' of the canonical correlation operator, that the number of zeros (counting multiplicities) on z = 1 of the transfer function, V(z), from innovations to outputs = (change in arg detE(z) around z = 1)/2[pi] = the number of unit Hankel singular values of E(s). It follows that the number of unit canonical correlations between the future x(t), t > 0 and the past x(t), t

Date: 1988
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