Practical problems with tests of cointegration rank with strong persistence and heavy-tailed errors: an application to the pricing of risk in the long run

We consider tests of cointegration between CDS prices and bond spreads in the heteroskedastic vector autoregressive (VAR) model. Strong persistence and very high persistence in volatility are stylised features of cointegrated systems of CDS prices and bond spreads. We show that tests of cointegration rank have low power under such conditions. One result from the power analysis is that obtaining high power requires more than 1000 observations, or more than four years of daily observations. There is empirical support that the distribution of the errors is heavy-tailed with infinite fourth moment. The asymptotic and bootstrap tests are invalid 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. We apply the WB test to daily observations from 2010 to 2016 on the CDS price and bond spread of US and European investment-grade firms. The WB test accepts cointegration for most firms in the full sample period. The evidence for cointegration is weak in sub-sample periods.