Estimating the Kronecker indices of cointegrated echelon form VARMA models

Cointegrated VARMA models can be parameterized by using the echelon form, which is characterized by the Kronecker indices. Three different methods for estimating the Kronecker indices of cointegrated echelon form VARMA models are discussed and compared. They have the common feature of estimating the individual equations of the system separately and using order selection criteria. The small sample performance of the methods is compared in a simulation study. It is found that the performance is better if all echelon form restrictions implied by the Kronecker indices found in preceeding steps are incorporated immediately.