The Nobel Prize in Economics awarded to Robert F. Engle and Clive W.J. Granger in 2003 recognized their groundbreaking work on co-integration and error correction. Their foundational article laid the groundwork for analyzing economic time series with a common trend, a concept that naturally extends the idea of economic equilibrium, especially when considering the non-stationarity of most macroeconomic variables. The article introduces the concept of co-integration, where a linear combination of non-stationary variables becomes stationary, leading to the notion of co-integrated variables. Engle and Granger's work significantly differs from classical econometrics, particularly in the methods used to handle non-stationary variables. They demonstrate that standard regression techniques can yield meaningful estimates even when variables are endogenous, and that direct and indirect regressions produce similar results, which is not the case in classical econometrics. The complexity of working with co-integration lies in the asymptotic distributions and critical values that differ from standard econometric practices. The authors propose a two-step estimation procedure for error correction models, which is asymptotically efficient and robust to the non-standard asymptotics and critical values. They also develop seven test statistics for testing co-integration, which are evaluated using Monte Carlo simulations. The tests are designed to maintain constant power across different parameterizations, making them suitable for a wide range of applications. The article highlights the importance of co-integration in macroeconometrics and time series theory, leading to significant contributions in areas such as stochastic volatility and Granger causality. Engle and Granger's work has had a profound impact on the field, influencing both theoretical and empirical research in economics and finance.The Nobel Prize in Economics awarded to Robert F. Engle and Clive W.J. Granger in 2003 recognized their groundbreaking work on co-integration and error correction. Their foundational article laid the groundwork for analyzing economic time series with a common trend, a concept that naturally extends the idea of economic equilibrium, especially when considering the non-stationarity of most macroeconomic variables. The article introduces the concept of co-integration, where a linear combination of non-stationary variables becomes stationary, leading to the notion of co-integrated variables. Engle and Granger's work significantly differs from classical econometrics, particularly in the methods used to handle non-stationary variables. They demonstrate that standard regression techniques can yield meaningful estimates even when variables are endogenous, and that direct and indirect regressions produce similar results, which is not the case in classical econometrics. The complexity of working with co-integration lies in the asymptotic distributions and critical values that differ from standard econometric practices. The authors propose a two-step estimation procedure for error correction models, which is asymptotically efficient and robust to the non-standard asymptotics and critical values. They also develop seven test statistics for testing co-integration, which are evaluated using Monte Carlo simulations. The tests are designed to maintain constant power across different parameterizations, making them suitable for a wide range of applications. The article highlights the importance of co-integration in macroeconometrics and time series theory, leading to significant contributions in areas such as stochastic volatility and Granger causality. Engle and Granger's work has had a profound impact on the field, influencing both theoretical and empirical research in economics and finance.