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BK

New Jersey : Princeton University Press, c1994

xiv, 799 s. ; 26 cm

ISBN 978-0-691-04289-3 (váz.) ISBN !0-691-04289-6 (chyb.)

Obsahuje bibliografie a rejstříky

000135336

PREFACE xii // 1 Difference Equations 1 // 1 i First-Order Difference Equations 1 1 2. pth-Order Difference Equations 7 // APPENDIX l.A. Proofs of Chapter 1 Propositions 21 References 24 // 2 Lag Operators 25 // 1. Introduction 25 // 1 I First-Order Difference Equations 27 // 2 Second-Order Difference Equations 29 // 2 - pth-Order Difference Equations 33 // 2 5 Initial Conditions and Unbounded Sequences 36 // References 42 // 3 Stationary ARMA Processes 43 // 3.1. Expectations, Stationarity, and Ergodicity 43 // 3.2. White Noise 47 // 3.3. Moving Average Processes 48 // 3.4. Autoregressive Processes 53 // 3.5. Mixed Autoregressive Moving Average Processes 59 // v // 3.6. The Autocovariance-Generating Function 61 // 3.7. Invertibility 64 // APPENDIX 3.A. Convergence Results for Infinite-Order Moving Average Processes 69 // Exercises 70 References 71 // 4 Forecasting 72 // 4.1. Principles of Forecasting 72 // 4.2. Forecasts Based on an Infinite Number of Observations 77 // 4.3. Forecasts Based on a Finite Number of Observations 85 // 4.4. The Triangular Factorization of a Positive Definite Symmetric Matrix 87 // 4.5. Updating a Linear Projection 92 // 4.6. Optimal Forecasts for Gaussian Processes 100 // 4.7. Sums of ARMA Processes 102 // 4.8. Wold’s Decomposition and the Box-Jenkins Modeling Philosophy 108 // APPENDIX 4.A. Parallel Between OLS Regression and Linear Projection 113 // APPENDIX 4.B. Triangular Factorization of the Covariance Matrix for an MA(1) Process 114 // Exercises 115 References 116 // 5 Maximum Likelihood Estimation 117 // 5.1. Introduction 117 // 5.2. The Likelihood Function for a Gaussian AR(l) // Process 118 // 5.3. The Likelihood Function for a Gaussian AR(p) Process 123 // 5.4. The Likelihood Function for a Gaussian MA(1) // Process 127 // 5.5. The Likelihood Function for a Gaussian MA(q) Process 130 //

5.6. The Likelihood Function for a Gaussian ARMA(p, q) Process 132 // 5.7. Numerical Optimization 133 // 5.8. Statistical Inference with Maximum Likelihood Estimation 142 // 5.9. Inequality Constraints 146 // APPENDIX 5. A. Proofs of Chapter 5 Propositions 148 Exercises 150 References 150 // 6 Spectral Analysis 152 // 6.1. 6.2. 6.3. 6.4. The Population Spectrum 152 The Sample Periodogram 158 Estimating the Population Spectrum 163 Uses of Spectral Analysis 167 // APPENDIX 6. A. Proofs of Chapter 6 Propositions 172 Exercises 178 References 178 // 7 Asymptotic Distribution Theory 180 // 7.1. 7.2. Review of Asymptotic Distribution Theory 180 Limit Theorems for Serially Dependent Observations 186 // APPENDIX 7. A. Proofs of Chapter 7 Propositions 195 Exercises 198 References 199 // 8 Linear Regression Models 200 // 8.1. Review of Ordinary Least Squares with Deterministic Regressors and i.i.d. Gaussian Disturbances 200 // 8.2. Ordinary Least Squares Under More General Conditions 207 // 8.3. Generalized Least Squares 220 // APPENDIX 8. A. Proofs of Chapter 8 Propositions 228 Exercises 230 References 231 // 9 Linear Systems of Simultaneous Equations 233 // 9.1. 9.2. Simultaneous Equations Bias 233 Instrumental Variables and Two-Stage Least Squares 238 // 9.3. Identification 243 // 9.4. Full-Information Maximum Likelihood Estimation 247 // 9.5. Estimation Based on the Reduced Form 250 // 9.6. Overview of Simultaneous Equations Bias 252 // APPENDIX 9. A. Proofs of Chapter 9 Proposition 253 Exercise 255 References 256 // 10 Covariance-Stationary Vector Processes 257 // 10.1. Introduction to Vector Autoregressions 257 // 10.2. Autocovariances and Convergence Results for Vector Processes 261 // 10.3. The Autocovariance-Generating Function for Vector Processes 266 // 10.4. The Spectrum for Vector Processes 268 // 10.5. The Sample Mean of a Vector Process 279 //

APPENDIX 10. A. Proofs of Chapter 10 Propositions 285 Exercises 290 References 290 // 11 Vector Autoregressions 291 // 11.1. Maximum Likelihood Estimation and Hypothesis Testing for an Unrestricted Vector Autoregression 291 // 11.2. Bivariate Granger Causality Tests 302 // 11.3. Maximum Likelihood Estimation of Restricted Vector Autoregressions 309 // 11.4. The Impulse-Response Function 318 // 11.5. Variance Decomposition 323 // 11.6. Vector Autoregressions and Structural Econometric Models 324 // 11.7. Standard Errors for Impulse-Response Functions 336 // APPENDIX 11. A. Proofs of Chapter 11 Propositions 340 APPENDIX 11.B. Calculation of Analytic Derivatives 344 Exercises 348 References 349 // 12 Bayesian Analysis 351 // 12.1. Introduction to Bayesian Analysis 351 // 12.2. Bayesian Analysis of Vector Autoregressions 360 // 12.3. Numerical Bayesian Methods 362 // APPENDIX 12.A. Proofs of Chapter 12 Propositions 366 Exercise 370 References 370 // 13 The Kalman Filter 372 // 13.1. The State-Space Representation of a Dynamic System 372 // 13.2. Derivation of the Kalman Filter ?11 // 13.3. Forecasts Based on the State-Space Representation 381 // 13.4. Maximum Likelihood Estimation of Parameters 385 // 13.5. The Steady-State Kalman Filter 389 // 13.6. Smoothing 394 // 13.7. Statistical Inference with the Kalman Filter 397 // 13.8. Time-Varying Parameters 399 // APPENDIX 13. A. Proofs of Chapter 13 Propositions 403 Exercises 406 References 407 // 14 Generalized Method of Moments 409 // 14.1. Estimation by the Generalized Method of Moments 409 // 14.2. Examples 415 // 14.3. Extensions 424 // 14.4. GMM and Maximum Likelihood Estimation 427 // APPENDIX 14. A. Proofs of Chapter 14 Propositions 431 Exercise 432 References 433 // 15 Models of Nonstationary Time Series // 15.1. Introduction 435 // 15.2. Why Linear Time Trends and Unit Roots? 438 //

15.3. Comparison of Trend-Stationary and Unit Root Processes 438 // 15.4. The Meaning of Tests for Unit Roots 444 // 15.5. Other Approaches to Trended Time Series 447 // APPENDIX 15. A. Derivation of Selected Equations for Chapter 15 451 References 452 // 16 Processes with Deterministic Time Trends 454 // 16.1. Asymptotic Distribution of OLS Estimates of the Simple Time Trend Model 454 // 16.2. Hypothesis Testing for the Simple Time Trend Model 461 // 16.3. Asymptotic Inference for an Autoregressive Process Around a Deterministic Time Trend 463 // APPENDIX 16. A. Derivation of Selected Equations for Chapter 16 472 // Exercises 474 References 474 // 17 Univariate Processes with Unit Roots 475 // 17.1. Introduction 475 // 17.2. Brownian Motion 477 // 17.3. The Functional Central Limit Theorem 479 // 17.4. Asymptotic Properties of a First-Order Autoregression when the True Coefficient Is Unity 486 // 17.5. Asymptotic Results for Unit Root Processes with General Serial Correlation 504 // 17.6. Phillips-Perron Tests for Unit Roots 506 // 17.7. Asymptotic Properties of a pth-Order Autoregression and the Augmented Dickey-Fuller Tests for Unit Roots 516 // 17.8. Other Approaches to Testing for Unit Roots 531 // 17.9. Bayesian Analysis and Unit Roots 532 // APPENDIX 17.A. Proofs of Chapter 17 Propositions 534 Exercises 537 References 541 // X Contents // 18 Unit Roots in Multivariate Time Series 544 // 18.1. Asymptotic Results for Nonstationary Vector Processes 544 // 18.2. Vector Autoregressions Containing Unit Roots 549 // 18.3. Spurious Regressions 557 // APPENDIX 18. A. Proofs of Chapter 18 Propositions 562 Exercises 568 References 569 // 19 Cointegration 571 // 19.1. Introduction 571 // 19.2. Testing the Null Hypothesis of No Cointegration 582 // 19.3. Testing Hypotheses About the Cointegrating Vector 601 //

APPENDIX 19. A. Proofs of Chapter 19 Propositions 618 Exercises 625 References 627 // 20 Full-Information Maximum Likelihood // Analysis of Cointegrated Systems 630 // 1. Canonical Correlation 630 // 1 2. Maximum Likelihood Estimation 635 // 2 .3. Hypothesis Testing 645 // 1 4. Overview of Unit Roots—To Difference or Not to Difference? 651 // APPENDIX 20.A. Proofs of Chapter 20 Propositions 653 Exercises 655 References 655 // 21 Time Series Models of Heteroskedasticity 657 // 21 1 Autoregressive Conditional Heteroskedasticity (ARCH) 657 :: 2. Extensions 665 // APPENDIX 21. A. Derivation of Selected Equations for Chapter 21 673 // References 674 // 22 Modeling Time Series with Changes // in Regime 677 // 22.1. Introduction 677 // 22.2. Markov Chains 678 // 22.3. Statistical Analysis of i.i.d. Mixture Distributions 685 // 22.4. Time Series Models of Changes in Regime 690 // APPENDIX 22. A. Derivation of Selected Equations // for Chapter 22 699 // Exercise 702 References 702 // A Mathematical Review 704 // A.l. Trigonometry 704 // A.2. Complex Numbers 708 // A.3. Calculus 711 // A.4. Matrix Algebra 721 // A.5. Probability and Statistics 739 // References 750 // B Statistical Tables 751 // C Answers to Selected Exercises 769 // D Greek Letters and Mathematical Symbols 786 // Used in the Text // AUTHOR INDEX 789 SUBJECT INDEX 792