Size and power of cointegration tests with non-normal GARCH error distributions

Abstract

Several tests for cointegration among non-stationary financial time series have been developed including the Dicky Fuller (1979) unit root tests, the Cointegration Regression Durbin-Watson test (1983), the Wild Bootstrap test (2003) and the Johansen likelihood ratio tests (1988). The Johensen’s tests appeared to provide superior results when the tests were originally applied to situations where the cointegration errors were normally distributed. However, substantial empirical evidences show that financial time series tend to be nonnormal in their distribution which may, in turn, lead to non-normal GARCH type cointegration error distributions. The question addressed in this paper is whether the Johansen’s
tests are still more powerful than the alternative tests when the underlying cointegration errors are non-normally distributed. Lee and Tse (1996) examined the performance of Johansen’s tests compared with DF tests and CRDW test when cointegration errors are fitted by GARCH(1,1) model with normal and student-t error distributions. This paper extends
their work. More cointegration tests with a wide range of error distributions are considered. Our simulation results indicate that the performance of power of the Johansen’s tests in capturing cointegration between financial time series is still higher than alternative tests even when the cointegration errors are not normally distributed (a skewed student-t distribution gives the best results). However, the best size performance is given by the Dicky Fuller test using the skewed generalized error distribution.