Estimating the Kronecker indices of cointegrated echelon‐form VARMA models

Abstract

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 echelon‐form VARMA models are discussed and compared. The three methods are expected to work even for non‐stationary processes with cointegrated variables. 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 for cointegrated systems. It is found that the performance is better if a sequential algorithm is used in which all echelon‐form restrictions implied by the Kronecker indices found in proceeding steps are incorporated.