  It is shown that in the multivariate case the orders p, of the AR part, and
q, of the MA part, are not invariants of the time series. Thus, it is concluded
that it only makes sense to define the class of ARMA(p,p)- irreducible models,
where p is the biggest of the system's Kronecker indices. This class is shown
not to be a differentiable manifold, but to contain one, which is a generic
subset of systems with all Kronecker indices equal to p. A formula which gives
the metric tensor for riemannian manifolds of linear systems as a line integral
in the complex plane is introduced for deterministic and stochastic cases and
some tensors are obtained with it.
