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• Half-title Page
• Title Page
• Copyright Page
• Contents
• Preface
• 1 Difference Equations
• 1.1. First-Order Difference Equations
• 1.2. pth-Order Difference Equations
• Appendix l.A. Proofs of Chapter 1 Propositions
• 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
• 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
• Exercises
• 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 ARMA 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
• Exercises
• References
• 5. Maximum Likelihood Estimation
• 5.1. Introduction
• 5.2. The Likelihood Function for a Gaussian AR() Process
• 5.3. The Likelihood Function for a Gaussian AR(p) Process
• 5.4. The Likelihood Function for a Gaussian MA(l) 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
• Exercises
• 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
• Exercises
• 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
• Exercises
• References
• 8. Linear Regression Models
• 8.1. Review of Ordinary Least Squares with Deterministic Regressors and i.i.d. GaussianDisturbances
• 8.2. Ordinary Least Squares Under More General Conditions
• 8.3. Generalized Least Squares
• Appendix 8. A. Proofs of Chapter 8 Propositions
• Exercises
• 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
• Exercise
• 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
• Exercises
• 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
• Exercises
• 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
• Exercise
• 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 of Parameters
• 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
• Exercises
• 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. Proofs of Chapter 14 Propositions
• Exercise
• 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
• 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
• Exercises
• 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 apth-Order Autoregression and the Augmented Dickey-Fuller Tests for U
• 17.8. Other Approaches to Testing for Unit Roots
• 17.9. Bayesian Analysis and Unit Roots
• Appendix 17.A. Proofs of Chapter 17 Propositions
• Exercises
• 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
• Exercises
• References
• 19. Cointegration
• 19.1. Introduction
• 19.2. Testing the Null Hypothesis of No Cointegration
• 19.3. Testing Hypotheses About the Cointegrating Vector
• Appendix 19. A. Proofs of Chapter 19 Propositions
• Exercises
• 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. Proofs of Chapter 20 Propositions
• Exercises
• 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
• 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
• Exercise
• References
• A. Mathematical Review
• A.I. Trigonometry
• A.2. Complex Numbers
• A.3. Calculus
• A.4. Matrix Algebra
• A.5. Probability and Statistics
• References
• B. Statistical Tables
• C. Answers to Selected Exercises
• D. Greek Letters and Mathematical Symbols Used in the Text
• Author Index
• Subject Index