Econometric Modelling with Time Series -...

Econometric Modelling with Time Series

This book provides a general framework for specifying, estimating and testingtime series econometric models. Special emphasis is given to estimation by maxi-mum likelihood, but other methods are also discussed, including quasi-maximumlikelihood estimation, generalized method of moments estimation, nonparamet-ric estimation and estimation by simulation. An important advantage of adoptingthe principle of maximum likelihood as the unifying framework for the book isthat many of the estimators and test statistics proposed in econometrics can bederived within a likelihood framework, thereby providing a coherent vehicle forunderstanding their properties and interrelationships. In contrast to many existingeconometric textbooks, which deal mainly with the theoretical properties of estim-ators and test statistics through a theorem-proof presentation, this book squarelyaddresses issues of implementation to provide a direct conduit between theory andapplied work. The comprehensive website accompanying this text may be found atwww.cambridge.org/econmodelling.

Vance Martin is Professor of Econometrics at the University of Melbourne,Australia, a position he has held since 2000. He graduated with a PhD from Mon-ash University in 1990. He was appointed a Lecturer at University of Melbourne in1985 and became a Senior Lecturer in 1990.

Stan Hurn is Professor of Economics and Finance at Queensland University ofTechnology, Australia, a position he has held since 1998. He graduated with aDPhil in Economics from St. Edmund Hall, Oxford, in 1992. He was appointed asa Lecturer at University of Glasgow in 1988 and became a Senior Lecturer in 1993before being named Official Fellow in Economics at Brasenose College, Oxford, in1996.

David Harris is Professor of Econometrics at Monash University, Australia. Hewas awarded his PhD in Econometrics from Monash University in 1995. He waslecturer in econometrics from 1995 to 1997 at Monash University and from 1998to 2010 at the University of Melbourne.

www.cambridge.org© in this web service Cambridge University Press

Cambridge University Press978-0-521-19660-4 - Econometric Modelling with Time Series: Specification, Estimation and TestingVance Martin, Stan Hurn and David HarrisFrontmatterMore information

http://www.cambridge.org/9780521196604

http://www.cambridge.org


Themes in Modern Econometrics

Managing EditorERIC GHYSELS, University of North Carolina, Chapel HillRICHARD J. SMITH, University of Cambridge

Series EditorPETER C. B. PHILLIPS, Yale University

Themes in Modern Econometrics is designed to service the large and grow-ing need for explicit teaching tools in econometrics. It provides an organizedsequence of textbooks in econometrics aimed squarely at the student popu-lation, and is the first series in the discipline to have this as its express aim.Written at a level accessible to students with an introductory course in econo-metrics behind them, each book addresses topics or themes that students andresearchers encounter daily. Although each book is designed to stand alone asan authoritative survey in its own right, the distinct emphasis throughout is onpedagogic excellence.

Titles in SeriesStatistics and Econometric Models: Volumes 1 and 2 CHRISTIAN

GOURIEROUX and ALAIN MONFORT Translated by QUANG VUONGTime Series and Dynamic Models CHRISTIAN GOURIEROUX and ALAIN

MONFORT Translated and edited by GIAMPIERO GALLOUnit Roots, Cointegration, and Structural Change G. S. MADDALA and

IN-MOO KIMGeneralized Method of Moments Estimation Edited by LASZLO MATYASNonparametric Econometrics ADRIAN PAGAN and AMAN ULLAHEconometrics of Qualitative Dependent Variables CHRISTIAN GOURIEROUX

Translated by PAUL B. KLASSENThe Econometric Analysis of Seasonal Time Series ERIC GHYSELS and

DENISE R. OSBORNSemiparametric Regression for the Applied Econometrician ADONIS

YATCHEWApplied Time Series Econometrics HELMUT LUTKEPOHL and MARKUS

KRATZIGIntroduction to the Mathematical and Statistical Foundations of Econometrics

HERMAN J. BIERENSEconomic Modeling and Inference JEAN-PIERRE FLORENS, VELAYOUDOM

MARIMOUTOU, and ANNE PEGUIN-FEISSOLLE Translated by JOSEFPERKTOLD and MARINE CARRASCO






ECONOMETRIC MODELLINGWITH TIME SERIES

Specification, Estimation and Testing

VANCE MARTINUniversity of Melbourne, Australia

STAN HURNQueensland University of Technology, Australia

DAVID HARRISMonash University, Australia






CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town,Singapore, Sao Paulo, Delhi, Mexico City

Cambridge University Press32 Avenue of the Americas, New York, NY 10013-2473, USA

www.cambridge.orgInformation on this title: www.cambridge.org/9780521139816

c© Vance Martin, Stan Hurn and David Harris 2013

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University Press.

First published 2013

Printed in the United States of America

A catalog record for this publication is available from the British Library.

Library of Congress Cataloging in Publication data

Martin, Vance, 1955–Econometric modelling with time series : specification, estimation and testing /Vance Martin, University of Melbourne, Australia, Stan Hurn, Queensland Universityof Technology, Australia, David Harris, Monash University, Australia.

p. cm. – (Themes in modern econometrics)Includes bibliographical references and index.ISBN 978-0-521-19660-4 (hardback) – ISBN 978-0-521-13981-6 (paperback)1. Econometric models. 2. Time-series analysis. I. Hurn, Stan. II. Harris,David, 1969– III. Title.HB141.M3555 2012330.01′51955–dc23 2012004347

ISBN 978-0-521-19660-4 HardbackISBN 978-0-521-13981-6 Paperback

Additional resources for this publication at www.cambridge.org/econmodelling

Cambridge University Press has no responsibility for the persistence or accuracy of URLs forexternal or third-party Internet websites referred to in this publication and does not guarantee thatany content on such websites is, or will remain, accurate or appropriate.






In memory of

Tim Monks (1961–1999), engineer, and

Simon Monks (1958–2007), physician. (S.H.)






Contents

List of Illustrations page xxiComputer Code Used in the Examples xxvPreface xxxi

PART ONE Maximum Likelihood

1 The Maximum Likelihood Principle 31.1 Introduction 31.2 Motivating Examples 31.3 Joint Probability Distributions 91.4 Maximum Likelihood Framework 11

1.4.1 The Log-Likelihood Function 121.4.2 Gradient 171.4.3 Hessian 19

1.5 Applications 221.5.1 Stationary Distribution of the Vasicek Model 231.5.2 Transitional Distribution of the Vasicek Model 24

1.6 Exercises 27

2 Properties of Maximum Likelihood Estimators 332.1 Introduction 332.2 Preliminaries 33

2.2.1 Properties of Stochastic Time Series 342.2.2 Weak Law of Large Numbers 382.2.3 Rates of Convergence 422.2.4 Central Limit Theorems 45

2.3 Regularity Conditions 532.4 Properties of the Likelihood Function 54

2.4.1 The Population Likelihood Function 54

ix






x Contents

2.4.2 Moments of the Gradient 552.4.3 The Information Matrix 58

2.5 Asymptotic Properties 602.5.1 Consistency 602.5.2 Normality 632.5.3 Efficiency 65

2.6 Finite-Sample Properties 682.6.1 Unbiasedness 692.6.2 Sufficiency 702.6.3 Invariance 712.6.4 Non-Uniqueness 72

2.7 Applications 722.7.1 Portfolio Diversification 742.7.2 Bimodal Likelihood 76

2.8 Exercises 78

3 Numerical Estimation Methods 873.1 Introduction 873.2 Newton Methods 88

3.2.1 Newton-Raphson 893.2.2 Method of Scoring 903.2.3 BHHH Algorithm 923.2.4 Comparative Examples 94

3.3 Quasi-Newton Methods 963.4 Line Searching 983.5 Optimisation Based on Function Evaluation 1003.6 Computing Standard Errors 1013.7 Hints for Practical Optimisation 104

3.7.1 Concentrating the Likelihood 1043.7.2 Parameter Constraints 1053.7.3 Choice of Algorithm 1063.7.4 Numerical Derivatives 1073.7.5 Starting Values 1083.7.6 Convergence Criteria 108

3.8 Applications 1093.8.1 Stationary Distribution of the CIR Model 1093.8.2 Transitional Distribution of the CIR Model 111

3.9 Exercises 112

4 Hypothesis Testing 1194.1 Introduction 1194.2 Overview 1194.3 Types of Hypotheses 121






Contents xi

4.3.1 Simple and Composite Hypotheses 1214.3.2 Linear Hypotheses 1224.3.3 Nonlinear Hypotheses 123

4.4 Likelihood Ratio Test 1244.5 Wald Test 128

4.5.1 Linear Hypotheses 1294.5.2 Nonlinear Hypotheses 130

4.6 Lagrange Multiplier Test 1314.7 Distribution Theory 133

4.7.1 Asymptotic Distribution of the Wald Statistic 1334.7.2 Asymptotic Relationships Among the Tests 1364.7.3 Finite Sample Relationships 138

4.8 Size and Power Properties 1394.8.1 Size of a Test 1394.8.2 Power of a Test 140

4.9 Applications 1414.9.1 Exponential Regression Model 1424.9.2 Gamma Regression Model 144

4.10 Exercises 147

PART TWO Regression Models

5 Linear Regression Models 1575.1 Introduction 1575.2 Specification 158

5.2.1 Model Classification 1585.2.2 Structural and Reduced Forms 160

5.3 Estimation 1625.3.1 Single Equation: Ordinary Least Squares 1625.3.2 Multiple Equations: FIML 1675.3.3 Identification 1715.3.4 Instrumental Variables 1735.3.5 Seemingly Unrelated Regression (SUR) Models 176

5.4 Testing 1775.5 Applications 183

5.5.1 Linear Taylor Rule 1835.5.2 The Klein Model of the United States Economy 184

5.6 Exercises 187

6 Nonlinear Regression Models 1946.1 Introduction 1946.2 Specification 1946.3 Maximum Likelihood Estimation 196






xii Contents

6.4 Gauss-Newton 2026.4.1 Relationship to Nonlinear Least Squares 2066.4.2 Relationship to Ordinary Least Squares 2076.4.3 Asymptotic Distributions 207

6.5 Testing 2086.5.1 LR, Wald and LM Tests 2086.5.2 Non-nested Tests 212

6.6 Applications 2156.6.1 Robust Estimation of the CAPM 2156.6.2 Stochastic Frontier Models 218

6.7 Exercises 222

7 Autocorrelated Regression Models 2287.1 Introduction 2287.2 Specification 2287.3 Maximum Likelihood Estimation 230

7.3.1 Exact Maximum Likelihood 2307.3.2 Conditional Maximum Likelihood 232

7.4 Alternative Estimators 2357.4.1 Gauss-Newton 2357.4.2 Zig-Zag Algorithms 2387.4.3 Cochrane-Orcutt 240

7.5 Distribution Theory 2427.5.1 Maximum Likelihood Estimator 2437.5.2 Least Squares Estimator 247

7.6 Lagged Dependent Variables 2517.7 Testing 252

7.7.1 Alternative LM Test I 2557.7.2 Alternative LM Test II 2567.7.3 Alternative LM Test III 257

7.8 Autocorrelation in Systems of Equations 2587.8.1 Estimation 2597.8.2 Testing 260

7.9 Applications 2617.9.1 Illiquidity and Hedge Funds 2617.9.2 Beach-MacKinnon Simulation Study 262

7.10 Exercises 263

8 Heteroskedastic Regression Models 2728.1 Introduction 2728.2 Specification 2728.3 Estimation 276






Contents xiii

8.3.1 Maximum Likelihood 2768.3.2 Relationship with Weighted Least Squares 279

8.4 Distribution Theory 2818.5 Testing 2828.6 Heteroskedasticity in Systems of Equations 288

8.6.1 Specification 2888.6.2 Estimation 2898.6.3 Testing 2918.6.4 Heteroskedastic and Autocorrelated

Disturbances 2928.7 Applications 294

8.7.1 The Great Moderation 2948.7.2 Finite Sample Properties of the Wald Test 295

8.8 Exercises 297

PART THREE Other Estimation Methods

9 Quasi-Maximum Likelihood Estimation 3079.1 Introduction 3079.2 Misspecification 3089.3 The Quasi-Maximum Likelihood Estimator 3129.4 Asymptotic Distribution 314

9.4.1 Misspecification and the Information Equality 3179.4.2 Independent and Identically Distributed Data 3209.4.3 Dependent Data and Martingale Difference Score 3229.4.4 Dependent Data and Score 322

9.5 Variance Estimation 3249.6 Quasi-Maximum Likelihood and Linear Regression 326

9.6.1 Misspecification: Non-normality 3299.6.2 Misspecification: Heteroskedasticity 3299.6.3 Misspecification: Autocorrelation 3319.6.4 The White Variance Estimator 3329.6.5 The Newey-West Variance Estimator 334

9.7 Testing 3389.8 Applications 339

9.8.1 Autoregressive Models for Count Data 3399.8.2 The CKLS Model of Interest Rates 342

9.9 Exercises 345

10 Generalised Method of Moments 35210.1 Introduction 35210.2 Motivating Examples 353






xiv Contents

10.2.1 Population Moments 35310.2.2 Empirical Moments 35410.2.3 GMM Models from Conditional Expectations 35810.2.4 GMM and Maximum Likelihood 361

10.3 Estimation 36210.3.1 The GMM Objective Function 36210.3.2 Asymptotic Properties 36410.3.3 Estimation Strategies 369

10.4 Over-identification Testing 37310.5 Applications 378

10.5.1 Monte Carlo Evidence 37810.5.2 Levels Effect in Interest Rates 381

10.6 Exercises 384

11 Nonparametric Estimation 39211.1 Introduction 39211.2 The Kernel Density Estimator 39311.3 Properties of the Kernel Density Estimator 397

11.3.1 Finite Sample Properties 39711.3.2 Optimal Bandwidth Selection 39811.3.3 Asymptotic Properties 40111.3.4 Dependent Data 403

11.4 Semi-parametric Density Estimation 40411.5 The Nadaraya-Watson Kernel Regression Estimator 40611.6 Properties of Kernel Regression Estimators 41011.7 Bandwidth Selection for Kernel Regression 41311.8 Multivariate Kernel Regression 41611.9 Semi-parametric Regression of the Partial Linear

Model 41811.10 Applications 419

11.10.1 Derivatives of a Nonlinear Production Function 42011.10.2 Drift and Diffusion Functions of SDEs 422

11.11 Exercises 424

12 Estimation by Simulation 43212.1 Introduction 43212.2 Motivating Example 43312.3 Indirect Inference 435

12.3.1 Estimation 43612.3.2 Relationship with Indirect Least Squares 439

12.4 Efficient Method of Moments (EMM) 44112.4.1 Estimation 44112.4.2 Relationship with Instrumental Variables 442






Contents xv

12.5 Simulated Generalised Method of Moments (SMM) 44412.6 Estimating Continuous-Time Models 445

12.6.1 Brownian Motion 44812.6.2 Geometric Brownian Motion 45112.6.3 Stochastic Volatility 454

12.7 Applications 45612.7.1 Finite Sample Properties 45712.7.2 Empirical Properties 459

12.8 Exercises 460

PART FOUR Stationary Time Series

13 Linear Time Series Models 46713.1 Introduction 46713.2 Time Series Properties of Data 46813.3 Specification 470

13.3.1 Univariate Model Classification 47113.3.2 Multivariate Model Classification 474

13.4 Stationarity 47613.4.1 The Stationarity Condition 47613.4.2 Wold’s Representation Theorem 47713.4.3 Transforming a VAR to a VMA 478

13.5 Invertibility 48113.5.1 The Invertibility Condition 48113.5.2 Transforming a VMA to a VAR 481

13.6 Estimation 48213.7 Optimal Choice of Lag Order 48613.8 Distribution Theory 48813.9 Testing 48913.10 Analysing Vector Autoregressions 491

13.10.1 Granger Causality Testing 49213.10.2 Impulse Response Functions 49313.10.3 Variance Decompositions 498

13.11 Applications 50013.11.1 Barro’s Rational Expectations Model 50113.11.2 The Campbell-Shiller Present Value Model 502

13.12 Exercises 504

14 Structural Vector Autoregressions 51214.1 Introduction 51214.2 Specification 513

14.2.1 Short-Run Restrictions 51614.2.2 Long-Run Restrictions 519






xvi Contents

14.2.3 Short-Run and Long-Run Restrictions 52214.2.4 Sign Restrictions 524

14.3 Estimation 52714.4 Identification 53114.5 Testing 53314.6 Applications 535

14.6.1 Peersman’s Model of Oil Price Shocks 53514.6.2 A Portfolio SVAR Model of Australia 537

14.7 Exercises 539

15 Latent Factor Models 54415.1 Introduction 54415.2 Motivating Examples 545

15.2.1 Empirical 54515.2.2 Theoretical 547

15.3 The Recursions of the Kalman Filter 54815.3.1 Univariate 54815.3.2 Multivariate 554

15.4 Extensions 55715.4.1 Intercepts 55715.4.2 Dynamics 55715.4.3 Nonstationary Factors 55815.4.4 Exogenous and Predetermined Variables 559

15.5 Factor Extraction 56015.6 Estimation 561

15.6.1 Identification 56115.6.2 Maximum Likelihood 56215.6.3 Principal Components Estimator 564

15.7 Relationship to VARMA Models 56615.8 Applications 567

15.8.1 The Hodrick-Prescott Filter 56715.8.2 A Factor Model of Spreads with Money Shocks 571

15.9 Exercises 573

PART FIVE Nonstationary Time Series

16 Nonstationary Distribution Theory 58316.1 Introduction 58316.2 Specification 584

16.2.1 Models of Trends 58416.2.2 Integration 586

16.3 Estimation 58816.3.1 Stationary Case 588






Contents xvii

16.3.2 Nonstationary Case: Stochastic Trends 59116.3.3 Nonstationary Case: Deterministic Trends 594

16.4 Asymptotics for Integrated Processes 59616.4.1 Brownian Motion 59716.4.2 Functional Central Limit Theorem 59816.4.3 Continuous Mapping Theorem 60216.4.4 Stochastic Integrals 603

16.5 Multivariate Analysis 60616.6 Applications 609

16.6.1 Least Squares Estimator of the AR(1) Model 60916.6.2 Trend Estimation in the Presence of a Random

Walk 61116.7 Exercises 613

17 Unit Root Testing 61917.1 Introduction 61917.2 Specification 61917.3 Detrending 621

17.3.1 Ordinary Least Squares (OLS) 62317.3.2 First Differences 62417.3.3 Generalised Least Squares (GLS) 625

17.4 Testing 62617.4.1 Dickey-Fuller Tests 62617.4.2 M Tests 627

17.5 Distribution Theory 62917.5.1 Ordinary Least Squares Detrending 63117.5.2 Generalised Least Squares Detrending 63217.5.3 Simulating Critical Values 634

17.6 Power 63617.6.1 Near Integration 63717.6.2 Asymptotic Local Power 63917.6.3 Point Optimal Tests 63917.6.4 Asymptotic Power Envelope 641

17.7 Autocorrelation 64217.7.1 Dickey-Fuller Test with Autocorrelation 64217.7.2 M Tests with Autocorrelation 643

17.8 Structural Breaks 64517.8.1 Known Break Point 64717.8.2 Unknown Break Point 651

17.9 Applications 65217.9.1 Power and the Initial Value 65217.9.2 Nelson-Plosser Data Revisited 653

17.10 Exercises 655






xviii Contents

18 Cointegration 66218.1 Introduction 66218.2 Long-Run Economic Models 66318.3 Specification of a VECM 665

18.3.1 Bivariate Models 66518.3.2 Multivariate Models 66718.3.3 Cointegration 66818.3.4 Deterministic Components 670

18.4 Estimation 67218.4.1 Full-Rank Case 67318.4.2 Reduced-Rank Case: Iterative Estimator 67418.4.3 Reduced-Rank Case: Johansen Estimator 67518.4.4 Zero-Rank Case 681

18.5 Identification 68218.5.1 Triangular Restrictions 68218.5.2 Structural Restrictions 683

18.6 Distribution Theory 68418.6.1 Asymptotic Distribution of the Eigenvalues 68418.6.2 Asymptotic Distribution of the Parameters 686

18.7 Testing 68918.7.1 Cointegrating Rank 69018.7.2 Cointegrating Vector 69318.7.3 Exogeneity 695

18.8 Dynamics 69618.8.1 Impulse Responses 69618.8.2 Cointegrating Vector Interpretation 697

18.9 Applications 69818.9.1 Rank Selection Based on Information Criteria 69818.9.2 Effects of Heteroskedasticity on the Trace Test 700

18.10 Exercises 701

PART SIX Nonlinear Time Series

19 Nonlinearities in Mean 71519.1 Introduction 71519.2 Motivating Examples 71519.3 Threshold Models 720

19.3.1 Specification 72019.3.2 Estimation 72219.3.3 Testing 723

19.4 Artificial Neural Networks 72619.4.1 Specification 72619.4.2 Estimation 728






Contents xix

19.4.3 Testing 73119.5 Bilinear Time Series Models 732


19.6 Markov Switching Model 73419.7 Nonparametric Autoregression 73819.8 Nonlinear Impulse Responses 74019.9 Applications 744

19.9.1 A Multiple Equilibrium Model of Unemployment 74419.9.2 Bivariate Threshold Models of G7 Countries 745

19.10 Exercises 748

20 Nonlinearities in Variance 75820.1 Introduction 75820.2 Statistical Properties of Asset Returns 75820.3 The ARCH Model 762


20.4 Univariate Extensions 76920.4.1 GARCH 76920.4.2 Integrated GARCH 77420.4.3 Additional Variables 77520.4.4 Asymmetries 77620.4.5 Garch-in-Mean 77720.4.6 Diagnostics 779

20.5 Conditional Non-normality 78020.5.1 Parametric 78020.5.2 Semi-parametric 78220.5.3 Nonparametric 783

20.6 Multivariate GARCH 78620.6.1 VECH 78720.6.2 BEKK 78820.6.3 DCC 79120.6.4 DECO 797

20.7 Applications 79820.7.1 DCC and DECO Models of United States Yields 79820.7.2 A Time-Varying Volatility SVAR Model 799

20.8 Exercises 802

21 Discrete Time Series Models 81221.1 Introduction 812






xx Contents

21.2 Motivating Examples 81221.3 Qualitative Data 815

21.3.1 Specification 81521.3.2 Estimation 81921.3.3 Testing 82221.3.4 Binary Autoregressive Models 824

21.4 Ordered Data 82621.5 Count Data 828

21.5.1 The Poisson Regression Model 83021.5.2 Integer Autoregressive Models 831

21.6 Duration Data 83521.7 Applications 837

21.7.1 An ACH Model of United States Airline Trades 83721.7.2 EMM Estimator of Integer Models 840

21.8 Exercises 842

Appendix A: Change of Variable in Density Functions 849

Appendix B: The Lag Operator 850B.1 Basics 850B.2 Polynomial Convolution 850B.3 Polynomial Inversion 851B.4 Polynomial Decomposition 852

Appendix C: FIML Estimation of a Structural Model 854C.1 Log-Likelihood Function 854C.2 First-Order Conditions 854C.3 Solution 855

Appendix D: Additional Nonparametric Results 857D.1 Mean 857D.2 Variance 859D.3 Mean Square Error 861D.4 Roughness 862

D.4.1 Roughness Results for the Gaussian Distribution 862D.4.2 Roughness Results for the Gaussian Kernel 863

References 865Author Index 877Subject Index 881






List of Illustrations

1.1 Probability distributions of yt for various models page 51.2 Probability distributions of yt for various models 71.3 Log-likelihood function for Poisson distribution 131.4 Log-likelihood function for exponential distribution 141.5 Log-likelihood function for the normal distribution 161.6 Eurodollar interest rates 221.7 Stationary density of Eurodollar interest rates 241.8 Transitional density of Eurodollar interest rates 262.1 Demonstration of the weak law of large numbers 392.2 Demonstration of the Lindeberg-Levy central limit theorem 462.3 Convergence of log-likelihood function 612.4 Consistency of sample mean for normal distribution 622.5 Consistency of median for Cauchy distribution 632.6 Illustrating asymptotic normality 652.7 Bivariate normal distribution 732.8 Scatterplot of returns on Apple and Ford stocks 742.9 Gradient of the bivariate normal model 773.1 Stationary density of Eurodollar interest rates: CIR model 1103.2 Estimated variance function of CIR model 1124.1 Illustrating the LR and Wald tests 1204.2 Illustrating the LM test 1204.3 Simulated and asymptotic distributions of the Wald test 1365.1 Simulating a bivariate regression model 1625.2 Sampling distribution of a weak instrument 1755.3 United States data on the Taylor Rule 1836.1 Simulated exponential models 1966.2 Scatterplot of Martin Marietta returns data 2166.3 Stochastic frontier disturbance distribution 2197.1 Simulated models with autocorrelated disturbances 230

xxi






xxii List of Illustrations

7.2 Distribution of maximum likelihood estimator in anautocorrelated regression model 246

8.1 Simulated data from heteroskedastic models 2758.2 The Great Moderation 2948.3 Sampling distribution of Wald test 2968.4 Power of Wald test 2979.1 Comparison of the true and misspecified log-likelihood

functions 3099.2 United States Dollar/British Pound exchange rates 3369.3 Estimated variance function of CKLS model 34410.1 Consistency of GMM 36611.1 Bias and variance of the kernel estimate of density 39811.2 Kernel estimate of distribution of stock index returns 40011.3 Bivariate normal density 40111.4 Semi-parametric density estimator 40511.5 Parametric conditional mean estimates 40611.6 Nadaraya-Watson nonparametric kernel regression 41011.7 Effect of bandwidth on kernel regression 41111.8 Bandwidth selection and cross-validation 41611.9 Two-dimensional product kernel 41711.10 Semi-parametric regression 41911.11 Nonparametric production function 42111.12 Nonparametric estimates of the drift and diffusion functions 42312.1 Simulated AR(1) model 43512.2 Illustrating Brownian motion 44613.1 United States macroeconomic data 46913.2 Plots of simulated stationary time series 47213.3 Choice of optimal lag order 48814.1 Bivariate SVAR model 51614.2 Bivariate SVAR with short-run restrictions 51914.3 Bivariate SVAR with long-run restrictions 52114.4 Bivariate SVAR with short- and long-run restrictions 52314.5 Bivariate SVAR with sign restrictions 52614.6 Impulse responses of Peersman’s model 53715.1 Daily United States zero coupon rates 54615.2 Alternative priors for latent factors in the Kalman filter 55915.3 Factor loadings of a term structure model 56515.4 Hodrick-Prescott filter of real United States GDP 57116.1 Nelson-Plosser data 58516.2 Simulated distribution of AR(1) parameter 59116.3 Continuous-time processes 60016.4 Functional Central Limit Theorem 60216.5 Distribution of a stochastic integral 606






List of Illustrations xxiii

16.6 Mixed normal distribution 60917.1 Real United States GDP 62017.2 Detrending 62617.3 Near unit root process 63717.4 Asymptotic power curve of ADF tests 64017.5 Asymptotic power envelope of ADF tests 64217.6 Structural breaks in United States GDP 64717.7 Union of rejections approach 65318.1 Permanent income hypothesis 66318.2 Long-run money demand 66418.3 Term structure of United States yields 66518.4 Error correction phase diagram 66619.1 Properties of an AR(2) model 71619.2 Limit cycle 71719.3 Strange attractor 71819.4 Nonlinear error correction model 71919.5 United States unemployment 71919.6 Threshold functions 72219.7 Decomposition of an ANN 72719.8 Simulated bilinear time series models 73319.9 Markov switching model of United States output 73819.10 Nonparametric estimate of a TAR(1) model 74019.11 Simulated TAR models for G7 countries 74720.1 Statistical properties of FTSE returns 75920.2 Distribution of FTSE returns 76220.3 News impact curve 76320.4 ACF of GARCH(1,1) models 77220.5 Conditional variance of FTSE returns 77420.6 BEKK model of United States zero coupon bonds 79020.7 DECO model of interest rates 80020.8 SVAR model of United Kingdom LIBOR spread 80221.1 United States Federal funds target rate from 1984 to 2009 81421.2 Money demand equation with a floor interest rate 81521.3 Duration descriptive statistics for AMR 838






Computer Code Used in theExamplesCode is written in GAUSS (*.g) , MATLAB (*.m) and in R (*.R)

1.1 basic sample.* 41.2 basic sample.* 51.3 basic sample.* 61.4 basic sample.* 61.5 basic sample.* 61.6 basic sample.* 71.7 basic sample.* 81.8 basic sample.* 81.10 basic poisson.* 131.11 basic exp.* 141.12 basic normal like.* 151.14 basic poisson.* 171.15 basic exp.* 181.16 basic normal like.* 181.17 basic poisson.* 201.18 basic exp.* 211.19 basic normal.* 212.5 prop wlln1.* 392.6 prop wlln2.* 402.8 prop moment.* 432.10 prop lindlevy.* 452.21 prop consistency.* 612.22 prop normal.* 622.23 prop cauchy.* 622.25 prop asymnorm.* 642.28 prop edgeworth.* 682.29 prop bias.* 703.2 max exp.* 893.3 max exp.* 913.4 max exp.* 93

xxv






xxvi Computer Code Used in the Examples

3.6 max weibull.* 953.7 max exp.* 973.8 max exp.* 993.9 max exp.* 1024.3 test weibull.* 1274.5 test weibull.* 1304.7 test weibull.* 1334.10 test asymptotic.* 1354.11 text size.* 1394.12 test power.* 1404.13 test power.* 1415.6 linear simulation.* 1615.7 linear estimate.* 1655.9 linear fiml.* 1705.11 linear weak.* 1745.15 linear estimate.* 1785.16 linear fiml.* 1816.3 nls simulate.* 1956.5 nls exponential.* 2006.7 nls consumption estimate.* 2046.8 nls contest.* 2086.11 nls money.* 2147.1 auto simulate.* 2297.5 auto invest.* 2347.8 auto distribution.* 2457.11 auto test.* 2537.12 auto system.* 2607.13 auto system.* 2608.1 hetero event.* 2738.2 hetero simulate.* 2748.4 hetero estimate.* 2778.7 hetero test.* 2868.9 hetero system.* 2908.10 hetero system.* 2918.11 hetero general.* 2939.1 qmle graph.* 3089.3 qmle graph.* 3099.19 qmle ar1reg.* 3349.20 qmle sf.* 3359.21 qmle sf.* 33910.1 gmm table.* 35610.2 gmm table.* 35710.3 gmm table.* 358






Computer Code Used in the Examples xxvii

10.8 gmm consistency.* 36510.10 gmm gamma.* 37210.11 gmm ccapm.* 37310.16 gmm ccapm.* 37711.1 npd kernel.* 39511.2 npd property.* 39811.3 npd ftse.* 40011.4 npd bivariate.* 40111.5 npd seminonlin.* 40511.6 npr parametric.* 40611.7 npr nadwatson.* 40911.8 npr property.* 41011.9 npr crossvalid.* 41511.10 npr bivariate.* 41711.11 npr semi.* 41912.1 sim mom.* 43512.3 sim accuracy.* 43712.4 sim ma1indirect.* 43912.5 sim ma1emm.* 44112.6 sim ma1overid.* 44512.7 sim brownind.*, sim brownemm.* 45013.1 stsm simulate.* 47113.8 stsm root.* 47713.9 stsm root.* 47713.17 stsm varma.* 48413.19 stsm recursive.* 48513.20 stsm laglength.* 48713.24 stsm recursive.* 49213.25 stsm recursive.* 49713.26 stsm recursive.* 49914.2 svar bivariate.* 51514.5 svar bivariate.* 51814.7 svar bivariate.* 52014.10 svar bivariate.* 52214.12 svar bivariate.* 52614.13 svar shortrun.* 52814.14 svar longrun.* 53014.15 svar recursive.* 53114.17 svar test.* 53314.18 svar test.* 53415.1 lfac termfig.* 54515.5 lfac uni.* 55315.6 lfac multi.* 555






xxviii Computer Code Used in the Examples

15.8 lfac smooth.* 56115.9 lfac uni.* 56215.10 lfac term.* 56315.11 lfac fvar.* 56415.12 lfac panic.* 56516.1 nts nelplos.* 58416.2 nts nelplos.* 58416.3 nts nelplos.* 58616.4 nts moment.*, nts distribution.* 59016.5 nts moment.* 59216.6 nts distribution.* 59316.7 nts yts.* 59916.8 nts fclt.* 60116.10 nts stochint.* 60416.11 nts stochint.* 60516.13 nts mixednormal.* 60817.1 unit qusgdp.* 62517.2 unit qusgdp.* 63517.3 unit asypower.* 63917.4 unit asypowerenv.* 64217.5 unit maicsim.* 64417.6 unit qusgdp.* 64617.7 unit breakeffect.* 64617.8 unit qusgdp.* 65017.9 unit qusgdp.* 65118.1 coint lrgraphs.* 66318.2 coint lrgraphs.* 66318.3 coint lrgraphs.* 66418.4 coint lrgraphs.* 66818.6 coint bivterm.* 67318.7 coint bivterm.* 67418.8 coint bivterm.* 67918.9 coint permincome.* 68018.10 coint bivterm.* 68118.11 coint triterm.* 68218.13 coint simevals.* 68518.14 coint bivterm.* 69118.15 coint triterm.* 69218.16 coint bivterm.* 69318.17 coint bivterm.* 69519.1 nlm features.* 71519.2 nlm features.* 71619.3 nlm features.* 717






Computer Code Used in the Examples xxix

19.4 nlm features.* 71719.5 nlm usrate.* 71819.6 nlm tarsim.* 72519.7 nlm annfig.* 72719.8 nlm bilinear.* 73219.9 nlm bcycle.* 73719.10 nlm tar.* 73919.11 nlm girf.* 74320.1 garch nic.* 76320.2 garch estimate.* 76620.3 garch test.* 76920.4 garch simulate.* 77120.5 garch estimate.* 77220.6 garch seasonality.* 77520.7 garch m.* 77820.8 garch studt.* 78520.9 mgarch bekk.* 79021.2 discrete mpol.* 81421.3 discrete floor.* 81421.4 discrete simulation.* 81821.7 discrete probit.* 82121.8 discrete probit.* 82421.9 discrete ordered.* 82721.11 discrete thinning.* 83221.12 discrete poissonauto.* 833

Code Disclaimer InformationNote that the computer code is provided for illustrative purposes only andalthough care has been taken to ensure that it works properly, it has not beenthoroughly tested under all conditions and on all platforms. The authors andCambridge University Press cannot guarantee or imply reliability, serviceabilityor function of this computer code. All code is therefore provided ‘as is’ withoutany warranties of any kind.






Econometric Modelling with Time Series -...

Documents

Transcript of Econometric Modelling with Time Series -...