["Oxford Bulletin of Economics and Statistics, EarlyView. ", "\nABSTRACT\nWe propose a two‐step procedure for detecting sparse cointegration in high‐dimensional single‐equation models. First, we employ the adaptive lasso to identify the subset of integrated covariates driving the long‐run equilibrium relationship. Second, we adopt an information‐theoretic criterion to distinguish between stationarity and nonstationarity in the resulting residuals, avoiding reliance on asymptotic distributions. A key theoretical contribution is demonstrating that this residual‐based decision rule remains consistent regardless of the internal cointegration structure among the right‐hand side predictors themselves. Monte Carlo experiments confirm the procedure's robust finite‐sample performance under endogeneity, serial correlation, and rank deficiency in the regressor matrix.\n"]