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Cover
Title Page
Copyright
Contents
Preface
About the Author
Chapter 1 Difference Equations
Introduction
1 Time-Series Models
2 Difference Equations and Their Solutions
3 Solution by Iteration
Iteration without an Initial Condition
Reconciling the Two Iterative Methods
Nonconvergent Sequences
4 An Alternative Solution Methodology
The Solution Methodology
Generalizing the Method
5 The Cobweb Model
6 Solving Homogeneous Difference Equations
Stability Conditions
Higher Order Systems
7 Particular Solutions for Deterministic Processes
8 The Method of Undetermined Coefficients
Higher Order Systems
A Solved Problem
9 Lag Operators
Lag Operators in Higher Order Systems
10 Summary
Questions and Exercises
Chapter 2 Stationary Time-Series Models
1 Stochastic Difference Equation Models
2 ARMA Models
3 Stationarity
Stationarity Restrictions for an AR(1) Process
4 Stationarity Restrictions for an ARMA (p, q) Model
Stationarity Restrictions for the Autoregressive Coefficients
5 The Autocorrelation Function
The Autocorrelation Function of an AR(2) Process
The Autocorrelation Function of an MA(1) Process
The Autocorrelation Function of an ARMA(1,1) Process
6 The Partial Autocorrelation Function
7 Sample Autocorrelations of Stationary Series
Model Selection Criteria
Estimation of an AR(1) Model
Estimation of an ARMA(1, 1) Model
Estimation of an AR(2) Model
8 Box-Jenkins Model Selection
Parsimony
Stationarity and Invertibility
Goodness of Fit
Postestimation Evaluation
9 Properties of Forecasts
Higher-Order Models
Forecast Evaluation
10 A Model of the Interest Rate Spread
Out-of-Sample Forecasts
11 Seasonality
Models of Seasonal Data
Seasonal Differencing
12 Parameter Instability and Structural Change
Testing for Structural Change
Endogenous Breaks
Parameter Instability
An Example of a Break
13 Combining Forecasts
Optimal Weights
Example Using the Spread
14 Summary and Conclusions
Questions and Exercises
Chapter 3 Modeling Volatility
1 Economic Time Series: The Stylized Facts
2 ARCH and GARCH Processes
ARCH Processes
The GARCH Model
3 ARCH and GARCH Estimates of Inflation
Engle’s Model of U.K. Inflation
Bollerslev’s Estimates of U.S. Inflation
4 Three Examples of GARCH Models
A GARCH Model of Oil Prices
Volatility Moderation
A GARCH Model of the Spread
Formal Tests for ARCH Errors
Alternative Estimates of the Model
5 A GARCH Model of Risk
6 The ARCH-M Model
Implementation
7 Additional Properties of GARCH Processes
Properties of GARCH(1, 1) Error Processes
Assessing the Fit
Diagnostic Checks for Model Adequacy
Forecasting the Conditional Variance
8 Maximum Likelihood Estimation of GARCH Models
9 Other Models of Conditional Variance
The IGARCH Model
Models with Explanatory Variables
Models with Asymmetry: TARCH and EGARCH
Testing for Leverage Effects
Nonnormal Errors
10 Estimating the NYSE U.S. 100 Index
The Model of the Mean
Testing for GARCH errors
Alternative Estimates of the Model
Diagnostic Checking
The Asymmetric Models
11 Multivariate GARCH
Updating the Study
12 Volatility Impulse Responses
An Example
13 Summary and Conclusions
Questions and Exercises
Chapter 4 Models with Trend
1 Deterministic and Stochastic Trends
The Random Walk Model
The Random Walk Plus Drift Model
Generalizations of the Stochastic Trend Model
2 Removing the Trend
Differencing
Detrending
Difference versus Trend Stationary Models
Are There Business Cycles?
The Trend in Real GDP
3 Unit Roots and Regression Residuals
4 The Monte Carlo Method
Monte Carlo Experiments
Example of the Monte Carlo Method
Generating the Dickey–Fuller Distribution
5 Dickey-Fuller Tests
An Example
6 Examples of the Dickey-Fuller Test
Quarterly Real U.S. GDP
Unit Roots and Purchasing Power Parity
7 Extensions of the Dickey-Fuller Test
Selection of the Lag Length
The Test with MA Components
Multiple Roots
Seasonal Unit Roots
8 Structural Change
Perron’s Test for Structural Change
Perron’s Test and Real Output
Tests with Simulated Data
9 Power and the Deterministic Regressors
Power
Determination of the Deterministic Regressors
10 Tests with More Power
An Example
11 Panel Unit Root Tests
Limitations of the Panel Unit Root Test
12 Trends and Univariate Decompositions
The General ARIMA(p, 1,q) Model
The Hodrick–Prescott Decomposition
13 Summary and Conclusions
Questions and Exercises
Chapter 5 Multiequation Time-Series Models
1 Intervention Analysis
Estimating the Effect of Metal Detectors on Skyjackings
Estimating the Effect of the Libyan Bombing
2 ADLs and Transfer Functions
ADL Models
The Cross-Covariances of a Second-Order Process
Higher-Order Input Processes
Identification and Estimation
3 An ADL of Terrorism in Italy
4 Limits to Structural Multivariate Estimation
Multivariate Macroeconometric Models: Some Historical Background
5 Introduction to VAR Analysis
Stability and Stationarity
Dynamics of a VAR Model
6 Estimation and Identification
Forecasting
Identification
7 The Impulse Response Function
Confidence Intervals and Impulse Responses
Variance Decomposition
8 Testing Hypotheses
Granger Causality
Granger Causality and Money Supply Changes
9 Example of a Simple VAR: Domestic and Transnational Terrorism
Empirical Methodology
Empirical Results
10 Structural VARs
Structural Decompositions
11 Examples of Structural Decompositions
12 Overidentified Systems
Two Examples
13 The Blanchard-Quah Decomposition
The Blanchard and Quah Results
14 Decomposing Real and Nominal Exchange Rates: An Example
Limitations of the Technique
15 Summary and Conclusions
Questions and Exercises
Chapter 6 Cointegration and Error-Correction Models
1 Linear Combinations of Integrated Variables
2 Cointegration and Common Trends
3 Cointegration and Error Correction
The n-Variable Case
4 Testing for Cointegration: The Engle-Granger Methodology
5 Illustrating the Engle-Granger Methodology
The Engle–Granger Procedure with I(2) Variables
6 Cointegration and Purchasing Power Parity
7 Characteristic Roots, Rank, and Cointegration
8 Hypothesis Testing
Lag Length and Causality Tests
To Difference or Not to Difference
Tests on Multiple Cointegrating Vectors
The Test in the Presence of I(2) Variables
9 Illustrating the Johansen Methodology
10 Error-Correction and ADL Tests
Cointegration with Weak Exogeneity
Inference on the Cointegrating Vector
11 Comparing the Three Methods
The Engle–Granger Methodology
The Johansen Methodology
The Error-Correction Methodology
12 Summary and Conclusions
Questions and Exercises
Chapter 7 Nonlinear Models and Breaks
1 Linear Versus Nonlinear Adjustment
2 Simple Extensions of the ARMA Model
The GAR Model
The Bilinear Model
An Example
3 Testing for Nonlinearity
The ACF and the McLeod–Li Test
The RESET
Other Portmanteau Tests
Lagrange Multiplier Tests
Two Examples
Inference with Unidentified Nuisance Parameters
4 Threshold Autoregressive Models
The Basic Threshold Model
Estimation
Unknown Threshold
5 Extensions of the TAR Model
Selecting the Delay Parameter
Multiple Regimes
More on Estimating the Threshold
Threshold Regression Models
Pretesting for a TAR Model
TAR Models and Endogenous Breaks
6 Three Threshold Models
The Unemployment Rate
Asymmetric Monetary Policy
Capital Stock Adjustment with Multiple Thresholds
7 Smooth Transition Models
Pretests for STAR Models
8 Other Regime Switching Models
The Artificial Neural Network
The Markov Switching Model
9 Estimates of STAR Models
An LSTAR Model
The Real Exchange Rate as an ESTAR Process
10 Generalized Impulse Responses and Forecasting
Nonlinear Estimates of GNP Growth
Impulse Responses
Terrorist Incidents with Casualties
11 Unit Roots and Nonlinearity
An Example
12 More on Endogenous Structural Breaks
Two Examples
Nonlinear Breaks
Estimates of a Logistic Break
13 Summary and Conclusions
Questions and Exercises
Index
EULA
Trim Size: 6in x 9in Enders bindex.tex V1 - 08/27/2014 6:48pm Page 486
Trim Size: 6in x 9in Enders ffirs.tex V1 - 08/21/2014 11:43am Page i FOURTH EDITION APPLIED ECONOMETRIC TIME SERIES WALTER ENDERS University of Alabama
Trim Size: 6in x 9in Enders ffirs.tex V1 - 09/02/2014 12:46pm Page ii Vice President and Executive Publisher Executive Editor Sponsoring Editor Project Editor Editorial Assistant Photo Editor Cover Designer Associate Production Manager Senior Production Editor Production Management Services Cover Image Credit George Hoffman Joel Hollenbeck Marian Provenzano Brian Baker Jacqueline Hughes Billy Ray Kenji Ngieng Joyce Poh Jolene Ling Laserwords Mmdi/Stone/Getty Images This book was set in 10/12 Times by Laserwords and printed and bound by Lightning Source. Founded in 1807, John Wiley & Sons, Inc. has been a valued source of knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations. Our company is built on a foundation of principles that include responsibility to the communities we serve and where we live and work. In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business. Among the issues we are addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and among our vendors, and community and charitable support. For more information, please visit our website: www.wiley.com/go/citizenship. Copyright © 2015, 2010, 2009, 1998 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923 (Web site: www.copyright.com). Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008, or online at: www.wiley.com/go/permissions. Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year. These copies are licensed and may not be sold or transferred to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return instructions and a free of charge return shipping label are available at: www.wiley.com/go/returnlabel. If you have chosen to adopt this textbook for use in your course, please accept this book as your complimentary desk copy. Outside of the United States, please contact your local sales representative. Library of Congress Cataloging-in-Publication Data Enders, Walter, 1948- Applied econometric time series / Walter, University of Alabama. – Fourth edition. pages cm Includes index. ISBN 978-1-118-80856-6 (pbk.) 1. Econometrics. 2. Time-series analysis. I. Title. HB139.E55 2015 330.01’519233–dc23 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 2014013428
Trim Size: 6in x 9in Enders ffirs.tex V1 - 08/21/2014 11:43am Page iii To Lola
Trim Size: 6in x 9in Enders ftoc.tex V1 - 08/21/2014 11:47am Page iv CONTENTS PREFACE vii ABOUT THE AUTHOR x CHAPTER 1 DIFFERENCE EQUATIONS 1 1 7 1 10 Introduction 1 Time-Series Models 2 Difference Equations and Their Solutions 3 Solution by Iteration 4 An Alternative Solution Methodology 5 The Cobweb Model 6 Solving Homogeneous Difference Equations 7 Particular Solutions for Deterministic Processes 8 The Method of Undetermined Coefficients 9 Lag Operators 10 Summary 40 43 14 18 22 31 34 Questions and Exercises 44 CHAPTER 2 STATIONARY TIME-SERIES MODELS 47 55 47 51 50 1 Stochastic Difference Equation Models 2 ARMA Models 3 Stationarity 4 Stationarity Restrictions for an ARMA (p, q) Model 60 5 The Autocorrelation Function 6 The Partial Autocorrelation Function 7 Sample Autocorrelations of Stationary Series 8 Box–Jenkins Model Selection 79 9 Properties of Forecasts 10 A Model of the Interest Rate Spread 11 Seasonality 12 Parameter Instability and Structural Change 13 Combining Forecasts 14 Summary and Conclusions 109 102 112 96 64 67 88 76 Questions and Exercises 113 iv
Trim Size: 6in x 9in Enders ftoc.tex V1 - 08/21/2014 11:47am Page v CHAPTER 3 MODELING VOLATILITY 118 CONTENTS v 141 134 130 123 1 Economic Time Series: The Stylized Facts 2 ARCH and GARCH Processes 3 ARCH and GARCH Estimates of Inflation 4 Three Examples of GARCH Models 5 A GARCH Model of Risk 6 The ARCH-M Model 7 Additional Properties of GARCH Processes 8 Maximum Likelihood Estimation of GARCH Models 9 Other Models of Conditional Variance 10 Estimating the NYSE U.S. 100 Index 165 11 Multivariate GARCH 12 Volatility Impulse Responses 13 Summary and Conclusions 154 158 172 174 143 118 146 152 Questions and Exercises 176 CHAPTER 4 MODELS WITH TREND 181 189 206 200 1 Deterministic and Stochastic Trends 2 Removing the Trend 3 Unit Roots and Regression Residuals 4 The Monte Carlo Method 5 Dickey–Fuller Tests 6 Examples of the Dickey–Fuller Test 7 Extensions of the Dickey–Fuller Test 8 Structural Change 9 Power and the Deterministic Regressors 10 Tests with More Power 11 Panel Unit Root Tests 12 Trends and Univariate Decompositions 13 Summary and Conclusions 238 243 227 254 181 195 210 215 235 247 Questions and Exercises 255 CHAPTER 5 MULTIEQUATION TIME-SERIES MODELS 259 267 277 261 1 Intervention Analysis 2 ADLs and Transfer Functions 3 An ADL of Terrorism in Italy 4 Limits to Structural Multivariate Estimation 5 Introduction to VAR Analysis 6 Estimation and Identification 7 The Impulse Response Function 8 Testing Hypotheses 9 Example of a Simple VAR: Domestic and Transnational Terrorism 309 10 Structural VARs 11 Examples of Structural Decompositions 12 Overidentified Systems 285 290 281 294 303 321 313 317
Trim Size: 6in x 9in Enders ftoc.tex V1 - 08/21/2014 11:47am Page vi vi CONTENTS 13 The Blanchard–Quah Decomposition 14 Decomposing Real and Nominal Exchange Rates: An Example 15 Summary and Conclusions 335 325 331 Questions and Exercises 337 CHAPTER 6 COINTEGRATION AND ERROR-CORRECTION MODELS 343 360 344 Illustrating the Engle–Granger Methodology 1 Linear Combinations of Integrated Variables 351 2 Cointegration and Common Trends 353 3 Cointegration and Error Correction 4 Testing for Cointegration: The Engle–Granger Methodology 5 6 Cointegration and Purchasing Power Parity 7 Characteristic Roots, Rank, and Cointegration 8 Hypothesis Testing 9 10 Error-Correction and ADL Tests 11 Comparing the Three Methods 12 Summary and Conclusions Illustrating the Johansen Methodology 400 380 364 370 373 389 393 397 Questions and Exercises 401 CHAPTER 7 NONLINEAR MODELS AND BREAKS 407 408 410 413 420 1 Linear Versus Nonlinear Adjustment 2 Simple Extensions of the ARMA Model 3 Testing for Nonlinearity 4 Threshold Autoregressive Models 5 Extensions of the TAR Model 6 Three Threshold Models 7 Smooth Transition Models 8 Other Regime Switching Models 9 Estimates of STAR Models 10 Generalized Impulse Responses and Forecasting 11 Unit Roots and Nonlinearity 12 More on Endogenous Structural Breaks 13 Summary and Conclusions 433 427 439 445 449 461 466 474 453 Questions and Exercises 475 INDEX 479 REFERENCES (ONLINE) ENDNOTES (ONLINE) STATISTICAL TABLES (ONLINE)
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