Time Series Analysis / / James Douglas Hamilton.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
• VerfasserIn: Hamilton, James Douglas,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2020]; ©1994
• Year of Publication: 2020
• Language: English
• Physical Description: 1 online resource (816 p.)

The last decade has brought dramatic changes in the way that researchers analyze economic and financial time series. This book synthesizes these recent advances and makes them accessible to first-year graduate students. James Hamilton provides the first adequate text-book treatments of important innovations such as vector autoregressions, generalized method of moments, the economic and statistical consequences of unit roots, time-varying variances, and nonlinear time series models. In addition, he presents basic tools for analyzing dynamic systems (including linear representations, autocovariance generating functions, spectral analysis, and the Kalman filter) in a way that integrates economic theory with the practical difficulties of analyzing and interpreting real-world data. Time Series Analysis fills an important need for a textbook that integrates economic theory, econometrics, and new results. The book is intended to provide students and researchers with a self-contained survey of time series analysis. It starts from first principles and should be readily accessible to any beginning graduate student, while it is also intended to serve as a reference book for researchers.

Table of Contents

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.

Time Series Models of Changes in Regime -- APPENDIX 22. A. Derivation of Selected Equations for Chapter 22 -- Chapter 22 Exercise -- Chapter 22 Reference -- A Mathematical Review -- A.1. Trigonometry -- A.2. Complex Numbers -- A.3. Calculus -- A.4. Matrix Algebra -- A.5. Probability and Statistics -- Appendix A References -- B Statistical Tables -- C Answers to Selected Exercises -- D Greek Letters and Mathematical Symbols Used in the Text -- Author Index -- Subject Index