Nonparametric tests for unit roots and cointegration

It is possible to construct unit root tests without specification of the short-run dynamics. These tests are robust against misspecification and structural breaks in the short-run components and can be used to test a wide range of nonlinear models. The variance ratio statistic is similar to the test statistic suggested by Kwiatkowski et al. (J. Econom. 15 (1992) 159) but assumes nonstationarity under the null hypothesis. A straightforward generalization of the variance ratio statistic is suggested, which can be used to test the cointegration rank in the spirit of Johansen (J. Econ. Dyn. Control 12 (1988) 231). Monte Carlo simulations suggest that the tests perform well in linear and nonlinear models with a sufficiently large sample size.