A Sieve Bootstrap Test for Cointegration in a Conditional Error Correction Model

In this paper we propose a bootstrap version of the Wald test for cointegration in a single-equation conditional error correction model. The multivariate sieve bootstrap is used to deal with dependence in the series. We show that the introduced bootstrap test is asymptotically valid. We also analyze the small sample properties of our test by simulation and compare it with the asymptotic test and several alternative bootstrap tests. The bootstrap test offers significant improvements in terms of size properties over the asymptotic test, while having similar power properties. The sensitivity of the bootstrap test to the allowance for deterministic components is also investigated. Simulation results show that the tests with sufficient deterministic components included are insensitive to the true value of the trends in the model and retain correct size.