When dynamic relations between time series have a finite dimension, they can be represented by means of transfer functions. One of the questions which then occur in this kind of modelling of multi-input-multi-output systems is the estimation of the orders of the polynomials so involved. Loosely speaking there are two main classes of methods. One in which one estimates the coefficients of the process, and the other one which involves indirect techniques related with Padé approximation. The authors give a characterization of the degrees in a minimal ARMA model through the observation of certain tables of values, which are built from the autocorrelations of the observed process.
Reviewer: G.Jumarie (Montreal)