Emory University

Residuals based tests for cointegration: an analytical comparison in the presence of deterministic trends.

Email address: epesave@emory.edu

Keywords: Cointegration, Unit roots, Local Power

JEL Classifications: C32

Abstract:
This paper proposes a careful comparison of residual based tests for the null of no cointegration and theorizes which unit root test should be used when testing for cointegration. In this non-standard environment, all tests have a non-normal asymptotic distribution and no uniformly most powerful test exists. For this reason, it is not clear which should be the best residual type test to be used to test for cointegration. To fully understand how these tests work and which parameters are important for power we need to look at their asymptotic distribution under close alternatives. Using local alternative parameterization, I compute the analytical power of five unit root tests applied to the residuals from a cointegration regression. The asymptotic distribution of the tests under the local alternative is shown to be a function of Brownian Motions and Ornstein-Uhlenbeck processes and to depend on a single nuisance parameter, which is, determined by the correlation at frequency zero of the independent variables with the errors of the cointegration regression. The tests are compared in term of power and size distortions and I show which kind of improvement can be achieved by using different unit root tests than the t-test originally proposed by Engle and Granger (1987). The tests are also compared for different detrending procedures for the cointegration regression.

PDF file of paper: Not available.

Session: Time Series Analysis

Time: Friday, 6 July, 8:45am - 10:15am

Room: B