Co-integration testing using local-to-unity detrending: the impact of structural change under the null

Abstract

In recent research, Perron and Rodriguez [Perron, P. and Rodriguez, G., 2006, Residual based tests for cointegration with GLS detrended data. Econometric Theory, in press.] have shown the use of local-to-unity detrending via generalised least squares to increase the power of the Engle–Granger [Engle, R. and Granger, C., 1987, Cointegration and error correction: representation, estimation and testing. Econometrica, 55, 251–276.] test for co-integration. In this paper, the properties of the resulting test are examined in the presence of structural change under the null hypothesis. The results of Monte Carlo experimentation show the test to possess very different properties to those noted in the literature previously by Leybourne and Newbold [Leybourne, S. and Newbold, P., 2003, Spurious rejections by co-integration tests induced by structural breaks. Applied Economics, 35, 1117–1121.] for the Engle–Granger and Johansen tests. The findings obtained show the extent of oversizing exhibited by the presence of level breaks to be substantially smaller than that of alternative co-integration tests. Furthermore, the results obtained for trend breaks are in stark contrast to those for alternative tests, with the oversizing noted for the Engle–Granger and Johansen tests replaced by undersizing for the test. In summary, the present analysis shows the test to be far less prone to the problem of spurious co-integration than previously examined tests.