Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models

TLDR

The paper develops likelihood-based methods for vector autoregressive models with cointegration. The authors derive likelihood ratio tests for cointegrating rank and structural hypotheses, showing the maximum likelihood estimator of the cointegrating relations follows a mixed Gaussian distribution that permits chi‑squared inference. © 1991 The Econometric Society.

Abstract

This paper contains the likelihood analysis of vector autoregressive models allowing for cointegration. The author derives the likelihood ratio test for cointegrating rank and finds it asymptotic distribution. He shows that the maximum likelihood estimator of the cointegrating relations can be found by reduced rank regression and derives the likelihood ratio test of structural hypotheses about these relations. The author shows that the asymptotic distribution of the maximum likelihood estimator is mixed Gaussian, allowing inference for hypotheses on the cointegrating relation to be conducted using the Chi( squared) distribution. Copyright 1991 by The Econometric Society.