An equivalent canonical form for multiple time series

In this paper, an equivalent canonical form VARTMA of multiple time series models is obtained by using the polynomial matrix theory, which may lead to converting the parameter estimation problem of the simultaneous equations into that of the single equation in modeling. It it proved that a VARMA model can be turned into the unique VARTMA form by means of the equivalence transformation, and the character of the transformed model is not changed at all.