On the identifiability of minimal VARMA representations (Q1281920)

It is well known that, in general, the minimal orders of VARMA processes are not unique. For example, a VARMA process may admit both an AR(1) and an MA(1) representation without being a white noise. The authors propose a way of finding all the minimal orders of the representations of VARMA processes in terms of the autocovariance function and a way of checking whether a representation with minimal orders is identifiable or not. Examples of VARMA processes with zero, one, or several standard identifiable representations are introduced.