Finance and Economics Discussion Series

Cointegration Test with Stationary Covariates and the CDS-Bond Basis during the Financial Crisis

Jason J. Wu and Aaron L. Game
2011-18

Abstract: This paper proposes a residual based cointegration test with improved power. Based on the idea of Hansen (1995) and Elliott & Jansson (2003) in the unit root testing case, stationary covariates are used to improve the power of the residual based Augmented Dickey Fuller (ADF) test. The asymptotic null distribution contains difficult to estimate nuisance parameters for which there is no obvious method of estimation, therefore we propose a bootstrap methodology to obtain test critical values. Local-to-unity asymptotics and Monte Carlo simulations are used to evaluate the power of the test in large and small samples, respectively. These exercises show that the addition of covariates increases power relative to the ADF and Johansen tests, and that the power depends on the long-run correlation between the covariates and the cointegration candidates. The new test is used to test for cointegration between Credit Default Swap (CDS) and corporate bond spreads for a panel of U.S. firms during the 2007-2009 financial crisis. The new test finds stronger evidence for cointegration between the two spreads for more firms, relative to ADF and Johansen tests.

Keywords: Cointegration, stationary covariates, local asymptotic power, CDS basis