This article introduces a testing procedure for cointegration and nonlinear adjustment in a smooth transition vector error correction model. To overcome the unidentified parameters problem under the null of no-cointegration, the Wald statistic is optimized over the unidentified parameter space. The asymptotic distribution of the test statistic is shown to be non-standard but nuisance parameter-free and hence critical values are obtained by simulations, Simulations show that the proposed test outperforms the alternatives in small sample sizes both in terms of size and power. Application to the exchange rate-monetary fundamentals relationship show that the proposed test works considerably well. This article also finds that nonlinear adjustment dynamics are symmetric for some currencies and therefore the speed of adjustment depends on the size of the deviations and is asymmetric for others, hence, the adjustment dynamics depend not only on the size but also on the sign of the deviations.