The influence of heteroskedastic variances on cointegration tests: A comparison using Monte Carlo simulations

Price cointegration between sovereign CDS and currency option markets in the financial crises of 2007–2013

“…Attfield (2003) finds that the Johansen cointegration test usually over-rejects the null hypothesis of no cointegration between multivariate time series in the presence of structural break or heteroskedasticity. Maki (2013) suggests that the Engle-Granger approach also suffers the same problem, however, it is generally regarded as one of the less problematic tests when the residual has a GARCH effect. His simulation results show that the empirical size is only slightly higher than the nominal size when using the Engle-Granger approach.…”

Statistical Arbitrage: A Critical View

“…These Quasi-LR tests use asymptotic critical values, which is reflected in moderate to high test-size distortions. In a simulation study of Johansen tests using innovations with an MGARCH type of conditional heteroscedasticity (Maki 2013), a true null hypothesis of no cointegration (r = 0) was more frequently rejected than the nominal critical level assumed.…”

“…Some cointegration tests assume in their alternative hypotheses models with a specific type of nonlinear error-correction and short-term dynamics, but according to simulations they suffer from unacceptably large test-size distortions under MGARCH heteroscedastic innovations (Maki 2013). It is of more benefit in the statistical arbitrage problem to use cointegration tests that do not require advance specification of the model dynamics.…”

“…According to the results of simulations (Maki 2013), the use of the Breitung cointegration test is recommended for samples of finite length, when the innovations are characterized by MGARCH conditional heteroscedasticity and a null hypothesis assumes no cointegration (the Breitung test has minimal size distortion among considered tests).…”