This is a summary of the book "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models" by Søren Johansen. The book provides a comprehensive statistical analysis of cointegration, which is a concept in time series analysis that describes long-run relationships between variables. The first part of the book focuses on the vector autoregressive (VAR) model, including its statistical analysis, misspecification tests, and illustrative examples. It then introduces the concepts of cointegration and integrated variables, explaining how to represent them in both autoregressive and moving average forms. The book then delves into the interpretation of I(1) models, which are models for variables that are integrated of order one, and discusses hypotheses on long-run and adjustment coefficients. It also covers the statistical analysis of I(1) models, hypothesis testing for long-run coefficients, partial systems, and the I(2) model, which is for variables integrated of order two. The second part of the book focuses on the probability analysis of cointegration, discussing the finite and asymptotic properties of I(1) processes, the asymptotic distribution of tests for cointegrating rank, and the determination of cointegrating rank. The third part includes appendices with mathematical results, weak convergence of probability measures, and stochastic integrals. The book is a detailed and comprehensive resource for understanding cointegration and its statistical analysis in time series models.This is a summary of the book "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models" by Søren Johansen. The book provides a comprehensive statistical analysis of cointegration, which is a concept in time series analysis that describes long-run relationships between variables. The first part of the book focuses on the vector autoregressive (VAR) model, including its statistical analysis, misspecification tests, and illustrative examples. It then introduces the concepts of cointegration and integrated variables, explaining how to represent them in both autoregressive and moving average forms. The book then delves into the interpretation of I(1) models, which are models for variables that are integrated of order one, and discusses hypotheses on long-run and adjustment coefficients. It also covers the statistical analysis of I(1) models, hypothesis testing for long-run coefficients, partial systems, and the I(2) model, which is for variables integrated of order two. The second part of the book focuses on the probability analysis of cointegration, discussing the finite and asymptotic properties of I(1) processes, the asymptotic distribution of tests for cointegrating rank, and the determination of cointegrating rank. The third part includes appendices with mathematical results, weak convergence of probability measures, and stochastic integrals. The book is a detailed and comprehensive resource for understanding cointegration and its statistical analysis in time series models.