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 is testing the approximate non-arbitrage relation between the credit default swap (CDS) price and bond spread. Strong persistence and very high persistence in volatility are stylised features of cointegrated systems of CDS prices and bond spreads. It is shown that tests of cointegration rank in the heteroskedastic vector autoregressive model have low power under such conditions. Obtaining high power requires more than 1000 observations. Hill estimates of the tail index indicate that the distribution of the errors has heavy tails with finite variance but infinite fourth moment. Asymptotic and bootstrap tests of cointegration rank 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 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.