Characterization o f the orders in VARMA models

Abstract

In tins paper we present a method which is able to identify the degrees of the matrix polynomials that are involved in the VARMA models. This method is based on the difference between the ranks of certain matrices defined from the sample covariance matrices of the process. The values of the mentioned difference are arranged in tabular from. The specific structure of this table lets us characterize a VARMA (p, q) model. We study the relative significance of certain elements to confirm the used pattern. The proposed procedure is illustrated by data simulations.