1. Introduction -- 2. The Notion of State -- 3. Data Generating Processes -- 3.1 Statistical Data Descriptions -- 3.2 Spectral Factorization -- 3.3 Decomposition of Time Series -- 3.4 Minimum-Phase Transfer Function Representation -- 4. State Space and ARMA Models -- 4.1 State Space Models -- 4.2 Conversion to State Space Representation -- 4.3 Conversion of State Space Models into ARMA Models -- 5. Properties of State Space Models -- 5.1 Observability -- 5.2 Orthogonal Projections -- 6. Hankel Matrix and Singular Value Decomposition -- 6.1 The Hankel Matrix -- 6.2 Singular Value Decomposition -- 6.3 Balanced Realization of State Space Model -- 6.4 Examples with Exact Covariance Matrices -- 6.5 Hankel Norm of a Transfer Function -- 6.6 Singular Value Decomposition in the z-Domain -- 7. Innovation Models, Riccati Equations, and Multiplier Analysis -- 7.1 Innovation Models -- 7.2 Solving Riccati Equations -- 7.3 Likelihood Functions -- 7.4 Dynamic Multiplier Analysis and Structural Model Identification -- 7.5 Out-of-Sample Forecasts -- 8. State Vectors and Optimality Measures -- 8.1 Canonical Variates -- 8.2 Prediction Error -- 8.3 Singular Values and Canonical Correlation Coefficients -- 9. Estimation of System Matrices -- 9.1 Two Classes of Estimators of System Matrices -- 9.2 Properties of Balanced Models -- 9.3 Examples with Exact Covariance Matrices -- 9.4 Numerical Examples -- 9.5 Monte Carlo Experiments -- 9.6 Model Selection -- 9.7 Incorporating Exogenous Variables -- 10. Approximate Models and Error Analysis -- 10.1 Structural Sensitivity -- 10.2 Error Norms -- 10.3 Asymptotic Error Covariance Matrices of Estimators -- 10.4 Other Statistical Aspects -- 11. Integrated Time Series -- 11.1 The Beveridge and Nelson Decomposition -- 11.2 State Space Decomposition -- 11.3 Contents of Random Walk Components -- 11.4 Cointegration, Error Correction, and Dynamic Aggregation -- 11.5 Two-Step Modeling Procedure -- 11.6 Dynamic Structure of Seasonal Components -- 11.7 Large Sample Properties -- 11.8 Drifts or Linear Deterministic Trends? -- 11.9 Regime Shifts -- 11.10 Nearly Integrated Processes -- 12. Numerical Examples -- 12.1 West Germany -- 12.2 United Kingdom -- 12.3 The United States of America -- 12.4 The US and West German Real GNP Interaction -- 12.5 The US and West German Real GNP and Unemployment Rate -- 12.6 The US and Japan Real GNP Interaction -- 12.7 The USA, West Germany, and Japan Real GNP Interaction -- 12.8 Further Examples -- Appendices -- A.1 Geometry of Weakly Stationary Stochastic Sequences -- A.2 The z-Transform -- A.3 Discrete and Continuous Time System Correspondences -- A.4 Some Useful Relations for Matrix Quadratic Forms -- A.5 Computation of Sample Covariance Matrices -- A.6 Properties of Symplectic Matrices -- A.7 Common Factors in ARMA Models -- A.8 Singular Value Decomposition Theorem -- A.9 Hankel Matrices -- A. 10 Spectral Factorization -- A.11 Time Series from Intertemporal Optimization -- A. 12 Time Series from Rational Expectations Models -- A. 13 Data Sources -- References.