Estimation and Testing for Unit Roots in a Partially Nonstationary Vector Autoregressive Moving Average Model

Abstract

The Gaussian estimation of a partially nonstationary autoregressive model and the related issue of testing for cointegration using the likelihood ratio test procedure have been considered by others. In this article we extend the Gaussian estimation procedure to partially nonstationary autoregressive moving average models and derive the asymptotic properties of the full-rank and reduced-rank Gaussian estimators. Based on these results, the asymptotic distribution of the likelihood ratio statistic for testing the number of unit roots is obtained. A numerical example based on three U.S. interest rate series is used to illustrate the estimation and testing procedures. The finite-sample properties of the estimation and likelihood ratio test procedures are examined through a small simulation study.