Frontmatter -- Contents -- Preface -- 1 Difference Equations -- 1.1. First-Order Difference Equations -- 1.2. pth-Order Difference Equations -- APPENDIX I.A. Proofs of Chapter 1 Propositions -- Chapter 1 References -- 2 Lag Operators -- 2.1. Introduction -- 2.2. First-Order Difference Equations -- 2.3. Second-Order Difference Equations -- 2.4. pth-Order Difference Equations -- 2.5. Initial Conditions and Unbounded Sequences -- Chapter 2 References -- 3 Stationary ARMA Processes -- 3.1. Expectations, Stationarity, and Ergodicity -- 3.2. White Noise -- 3.3. Moving Average Processes -- 3.4. Autoregressive Processes -- 3.5. Mixed Autoregressive Moving Average Processes -- 3.6. The Autocovariance-Generating Function -- 3.7. Invertibility -- APPENDIX 3.A. Convergence Results for Infinite-Order Moving Average Processes -- Chapter 3 Exercises -- Chapter 3 References -- 4 Forecasting -- 4.1. Principles of Forecasting -- 4.2. Forecasts Based on an Infinite Number of Observations -- 4.3. Forecasts Based on a Finite Number of Observations -- 4.4. The Triangular Factorization of a Positive Definite Symmetric Matrix -- 4.5. Updating a Linear Projection -- 4.6. Optimal Forecasts for Gaussian Processes -- 4.7. Sums of ARM A Processes -- 4.8. Wold's Decomposition and the Box-Jenkins Modeling Philosophy -- APPENDIX 4.A. Parallel Between OLS Regression and Linear Projection -- APPENDIX 4.B. Triangular Factorization of the Covariance Matrix for an MA(1) Process -- Chapter 4 Exercises -- Chapter 4 References -- 5 Maximum Likelihood Estimation -- 5.1. Introduction -- 5.2. The Likelihood Function for a Gaussian AR(7J Process -- 5.3. The Likelihood Function for a Gaussian AR(p) Process -- 5.4. The Likelihood Function for a Gaussian MA(1) Process -- 5.5. The Likelihood Function for a Gaussian MA(q) Process -- 5.6. The Likelihood Function for a Gaussian ARMA(p, q) Process -- 5.7. Numerical Optimization -- 5.8. Statistical Inference with Maximum Likelihood Estimation -- 5.9. Inequality Constraints -- APPENDIX 5. A. Proofs of Chapter 5 Propositions -- Chapter 5 Exercises -- Chapter 5 References -- 6 Spectral Analysis -- 6.1. The Population Spectrum -- 6.2. The Sample Periodogram -- 6.3. Estimating the Population Spectrum -- 6.4. Uses of Spectral Analysis -- APPENDIX 6. A. Proofs of Chapter 6 Propositions -- Chapter 6 Exercises -- Chapter 6 References -- 7 Asymptotic Distribution Theory -- 7.1. Review of Asymptotic Distribution Theory -- 7.2. Limit Theorems for Serially Dependent Observations -- APPENDIX 7.A. Proofs of Chapter 7 Propositions -- Chapter 7 Exercises -- Chapter 7 Exercises -- 8 Linear Regression Models -- 8.1. Review of Ordinary Least Squares with Deterministic Regressors and i.i.d. Gaussian Disturbances -- 8.2. Ordinary Least Squares Under More General Conditions -- 8.3. Generalized Least Squares -- APPENDIX 8. A. Proofs of Chapter 8 Propositions -- Chapter 8 Exercises -- Chapter 8 References -- 9 Linear Systems of Simultaneous Equations -- 9.1. Simultaneous Equations Bias -- 9.2. Instrumental Variables and Two-Stage Least Squares -- 9.3. Identification -- 9.4. Full-Information Maximum Likelihood Estimation -- 9.5 Estimation Based on the Reduced Form -- 9.6. Overview of Simultaneous Equations Bias -- APPENDIX 9.A. Proofs of Chapter 9 Proposition -- Chapter 9 Exercise -- Chapter 9 References -- 10 Covariance-Stationary Vector Processes -- 10.1. Introduction to Vector Autoregressions -- 10.2. Autocovariances and Convergence Results for Vector Processes -- 10.3. The Autocovariance-Generating Function for Vector Processes -- 10.4. The Spectrum for Vector Processes -- 10.5. The Sample Mean of a Vector Process -- APPENDIX 10.A. Proofs of Chapter 10 Propositions -- Chapter 10 Exercises -- Chapter 10 References -- 11 Vector Autoregressions -- 11.1. Maximum Likelihood Estimation and Hypothesis Testing for an Unrestricted Vector Autoregression -- 11.2. Bivariate Granger Causality Tests -- 11.3. Maximum Likelihood Estimation of Restricted Vector Autoregressions -- 11.4. The Impulse-Response Function -- 11.5. Variance Decomposition -- 11.6. Vector Autoregressions and Structural Econometric Models -- 11.7. Standard Errors for Impulse-Response Functions -- APPENDIX 11. A. Proofs of Chapter 11 Propositions -- APPENDIX 11.B. Calculation of Analytic Derivatives -- Chapter 11 Exercises -- Chapter 11 References -- 12 Bayesian Analysis -- 12.1. Introduction to Bayesian Analysis -- 12.2. Bayesian Analysis of Vector Autoregressions -- 12.3. Numerical Bayesian Methods -- APPENDIX 12.A. Proofs of Chapter 12 Propositions -- Chapter 12 Exercise -- Chapter 12 References -- 13 The Kalman Filter -- 13.1. The State-Space Representation of a Dynamic System -- 13.2. Derivation of the Kalman Filter -- 13.3. Forecasts Based on the State-Space Representation -- 13.4. Maximum Likelihood Estimation -- 13.5. The Steady-State Kalman Filter -- 13.6. Smoothing -- 13.7. Statistical Inference with the Kalman Filter -- 13.8. Time-Varying Parameters -- APPENDIX 13. A. Proofs of Chapter 13 Propositions -- Chapter 13 Exercises -- Chapter 13 References -- 14 Generalized Method of Moments -- 14.1. Estimation by the Generalized Method of Moments -- 14.2. Examples -- 14.3. Extensions -- 14.4. GMM and Maximum Likelihood Estimation -- APPENDIX 14. A. Proof of Chapter 14 Proposition -- Chapter 14 Exercise -- Chapter 14 References -- 15 Models of Nonstationary Time Series -- 15.1. Introduction -- 15.2. Why Linear Time Trends and Unit Roots? -- 15.3. Comparison of Trend-Stationary and Unit Root Processes -- 15.4. The Meaning of Tests for Unit Roots -- 15.5. Other Approaches to Trended Time Series -- APPENDIX 15. A. Derivation of Selected Equations for Chapter 15 -- Chapter 15 References -- 16 Processes with Deterministic Time Trends -- 16.1. Asymptotic Distribution of OLS Estimates of the Simple Time Trend Model -- 16.2. Hypothesis Testing for the Simple Time Trend Model -- 16.3. Asymptotic Inference for an Autoregressive Process Around a Deterministic Time Trend -- APPENDIX 16. A. Derivation of Selected Equations for Chapter 16 -- Chapter 16 Exercises -- Chapter 16 References -- 17 Univariate Processes with Unit Roots -- 17.1. Introduction -- 17.2. Brownian Motion -- 17.3. The Functional Central Limit Theorem -- 17.4. Asymptotic Properties of a First-Order Autoregression when the True Coefficient Is Unity -- 17.5. Asymptotic Results for Unit Root Processes with General Serial Correlation -- 17.6. Phillips-Perron Tests for Unit Roots -- 17.7. Asymptotic Properties of a pth-Order Autoregression and the Augmented Dickey-Fuller Tests for Unit Roots -- 17.8. Other Approaches to Testing for Unit Roots -- 17.9. Bayesian Analysis and Unit Roots -- APPENDIX 17.A. Proofs of Chapter 17 Propositions -- Chapter 17 Exercises -- Chapter 17 References -- 18 Unit Roots in Multivariate Time Series -- 18.1. Asymptotic Results for Nonstationary Vector Processes -- 18.2. Vector Autoregressions Containing Unit Roots -- 18.3. Spurious Regressions -- APPENDIX 18.A. Proofs of Chapter 18 Propositions -- Chapter 18 Exercises -- Chapter 18 References -- 19 Cointegration -- 19.1. Introduction -- 19.2. Testing the Null Hypothesis -- 19.3. Testing Hypotheses About the Cointegrating Vector -- APPENDIX 19. A. Proofs of Chapter 19 Propositions -- Chapter 19 Exercises -- Chapter 19 References -- 20 Full-Information Maximum Likelihood Analysis of Cointegrated Systems -- 20.1. Canonical Correlation -- 20.2. Maximum Likelihood Estimation -- 20.3. Hypothesis Testing -- 20.4. Overview of Unit Roots—To Difference or Not to Difference? -- APPENDIX 20.A. Proof of Chapter 20 Proposition -- Chapter 20 Exercises -- Chapter 20 References -- 21 Time Series Models of Heteroskedasticity -- 21.1. Autoregressive Conditional Heteroskedasticity (ARCH) -- 21.2. Extensions -- APPENDIX 21. A. Derivation of Selected Equations for Chapter 21 -- Chapter 21 References -- 22 Modeling Time Series with Changes in Regime -- 22.1. Introduction -- 22.2. Markov Chains -- 22.3. Statistical Analysis of i.i.d. Mixture Distributions -- 22.4.
