The book "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models" by Søren Johansen, published by Oxford University Press in 1995, provides a comprehensive analysis of cointegration in vector autoregressive (VAR) models. The content is divided into three main parts: statistical analysis of cointegration, probability analysis of cointegration, and appendices. - **Introduction**: Discusses the vector autoregressive model, building statistical models, and illustrative examples. - **The Vector Autoregressive Model**: Explains the vector autoregressive process, statistical analysis, misspecification tests, and illustrative examples. - **Basic Definitions and Concepts**: Introduces cointegration and common trends. - **Cointegration and Representation of Integrated Variables**: Covers the representation of I(1) and I(2) variables. - **The I(1) Models and Their Interpretation**: Focuses on cointegration models, parametrization, hypotheses, and structural error correction models. - **The Statistical Analysis of I(1) Models**: Discusses likelihood analysis, deterministic drift terms, determination of cointegrating rank, and exercises. - **Hypothesis Testing for the Long Run Coefficients β**: Covers degrees of freedom, linear restrictions, illustrative examples, and exercises. - **Partial Systems and Hypotheses on α**: Introduces partial systems, test of restrictions on α, and the duality between β and α⊥. - **The I(2) Model and a Test for I(2)**: Provides a statistical model for I(2), a misspecification test, and a test for I(2) in Australian data. - **Probability Properties of I(1) Processes**: Discusses finite sample and asymptotic results. - **The Asymptotic Distribution of the Test for Cointegrating Rank**: Explains testing H = 0, the limit distribution, and asymptotic properties. - **Determination of Cointegrating Rank**: Focuses on models without, with, and including deterministic terms. - **Consistency of Estimators and Asymptotic Distributions**: Introduces the mixed Gaussian distribution, consistency of estimators, and asymptotic distributions. - **Local Alternatives and Power Functions**: Discusses local alternatives, properties under local alternatives, and the power of the trace test. - **Simulation of the Limit Distribution and Power Function**: Provides simulations and tables. - **Mathematical Results**: Covers eigenvalues, eigenvectors, the binomial formula for matrices, multivariate Gaussian distribution, and principal components. - **Weak Convergence of Probability Measures**: Discusses weak convergence on R^p and C[0,1], construction of measures, tightness, and Prohorov's theorem. - **Construction of Brownian Motion and Stochastic Integrals**: Introduces Brownian motion and stochastic integrals. -The book "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models" by Søren Johansen, published by Oxford University Press in 1995, provides a comprehensive analysis of cointegration in vector autoregressive (VAR) models. The content is divided into three main parts: statistical analysis of cointegration, probability analysis of cointegration, and appendices. - **Introduction**: Discusses the vector autoregressive model, building statistical models, and illustrative examples. - **The Vector Autoregressive Model**: Explains the vector autoregressive process, statistical analysis, misspecification tests, and illustrative examples. - **Basic Definitions and Concepts**: Introduces cointegration and common trends. - **Cointegration and Representation of Integrated Variables**: Covers the representation of I(1) and I(2) variables. - **The I(1) Models and Their Interpretation**: Focuses on cointegration models, parametrization, hypotheses, and structural error correction models. - **The Statistical Analysis of I(1) Models**: Discusses likelihood analysis, deterministic drift terms, determination of cointegrating rank, and exercises. - **Hypothesis Testing for the Long Run Coefficients β**: Covers degrees of freedom, linear restrictions, illustrative examples, and exercises. - **Partial Systems and Hypotheses on α**: Introduces partial systems, test of restrictions on α, and the duality between β and α⊥. - **The I(2) Model and a Test for I(2)**: Provides a statistical model for I(2), a misspecification test, and a test for I(2) in Australian data. - **Probability Properties of I(1) Processes**: Discusses finite sample and asymptotic results. - **The Asymptotic Distribution of the Test for Cointegrating Rank**: Explains testing H = 0, the limit distribution, and asymptotic properties. - **Determination of Cointegrating Rank**: Focuses on models without, with, and including deterministic terms. - **Consistency of Estimators and Asymptotic Distributions**: Introduces the mixed Gaussian distribution, consistency of estimators, and asymptotic distributions. - **Local Alternatives and Power Functions**: Discusses local alternatives, properties under local alternatives, and the power of the trace test. - **Simulation of the Limit Distribution and Power Function**: Provides simulations and tables. - **Mathematical Results**: Covers eigenvalues, eigenvectors, the binomial formula for matrices, multivariate Gaussian distribution, and principal components. - **Weak Convergence of Probability Measures**: Discusses weak convergence on R^p and C[0,1], construction of measures, tightness, and Prohorov's theorem. - **Construction of Brownian Motion and Stochastic Integrals**: Introduces Brownian motion and stochastic integrals. -