The statistical theory of linear systems
The statistical theory of linear systems
Rationality, minimality and uniqueness of representation of matrix formal power series
Journal of Computational and Applied Mathematics
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
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The identification stage of Vector Autoregressive Moving Average (VARMA) models plays an important role in multivariate time series analysis and it has been discussed from different approaches in literature. In particular, the notion of Scalar Component Model (SCM) is highly ingenious and emerges in [7] as a fairly natural way of modelling multivariate time series. The idea of SCM is of enormous benefit because the effect is the reduction of parameters in VARMA representation and it could simplified drastically the complexity in estimation. In the procedure to identify SCMs ([7]), the authors use subjective choices of a parameter denoted by h. Varying the value of h is likely to result in substantially different orders for the SCM. Then, of great interest is the question about how robust is the identification procedure with regard to the choice of h. Therefore, the aim of this paper is to find necessary and sufficient conditions to choose the minimum value of h, such that the procedure to identify SCMs will not lead to theoretical errors.