Practical Problems with Tests of Cointegration Rank with Strong Persistence and Heavy-Tailed Errors

Financial time series have several distinguishing features which are of concern in tests of cointegration. An example considered in this paper is testing the approximate non-arbitrage relation between the credit default swap (CDS) price and bond spread. We show that strong persistence and very high persistence in volatility are stylised features of cointegrated systems of CDS prices and bond spreads. There is empirical support that the distribution of the errors is heavy-tailed with infinite fourth moment. Tests for cointegration have low power under such conditions. The asymptotic and bootstrap tests are unreliable if the errors are heavy-tailed with infinite fourth moment. Monte Carlo simulations indicate that the wild bootstrap (WB) test may be justified with heavy-tailed errors which do not have finite fourth moment. The tests are applied to CDS prices and bond spreads of US and European investment-grade firms.