This study introduces a cointegration test based on an asymmetric exponential smooth transition autoregressive (AESTAR) error correction model (ECM). The proposed model based on the unit root test by Sollis (2009) employs a wild bootstrap to test for cointegration. The test has time-varying and asymmetric adjustments and is robust to heteroskedastic variances such as stochastic volatility. A Monte Carlo simulation provides evidence that the proposed test has appropriate sizes and sufficient power under stochastic volatility. The model is applied to the relationship between the oil price and economic activity, demonstrating that the proposed test supports the presence of the error correction term. This contrasts with conventional tests, which do not support this term. The empirical results indicate the usefulness of the proposed test.