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Summary: Inspired by constructing large‐size cointegrated portfolios, this paper considers a vector error correction model and develops the adaptive Lasso estimator of the cointegrating vectors. The asymptotic properties of the estimators and the oracle property of the adaptive Lasso are derived. An optimisation algorithm for estimating the model parameters is proposed. The simulation study shows the effectiveness of the parameter estimation procedures and the forecasting performance of our model. In the empirical study, we apply the proposed method to construct the sparse cointegrated portfolios with or without market‐neutral property. The trading performances of different types of cointegrated portfolios are evaluated using the Dow Jones Industrial Average composite stocks. The empirical findings reveal that the sparse cointegrated market‐neutral portfolios of a number of securities are capable to benefit the investors who wish to construct statistical arbitrage portfolios which are market‐neutral. [ABSTRACT FROM AUTHOR]