Identifiability and Minimality in Rational Models

Celina Pestano-Gabino, Concepción González-Concepción, María Candelaria Gil-Fariña

Abstract

This paper uses key algebraic relationships between matrix Padé approximation and certain multivariate time series models. These relationships help us to obtain relevant results for solving the problems of identifiability and exchangeability in several models. We develop a new generalization of the corner method and apply it to the multivariate case. One advantage of the procedure is the presentation of the results in easily interpretable tables. We define new canonical representations. The paper also contains additional theoretical results improving on formulations of the corresponding algorithm that will assist us. The technique is illustrated in Vectorial Autoregressive Moving Average models by using a theoretical example.

Keywords

Matrix Padé approximation; Multivariate time series; Rational models; Specification stage; exchangeability; Identifiability

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