A Covariate Residual-Based Cointegration Test Applied to the CDS-Bond Basis

This paper proposes a residual-based cointegration test with improved power. Based on the idea of Hansen (1995) and Elliot and 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 difficulty 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 US 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.