APPLIED TIME SERIES Applied Time Series Econometrics Time series econometrics is a rapidly evolving

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    Applied Time Series Econometrics

    Time series econometrics is a rapidly evolving field. In particular, the cointegration revolution has had a substantial impact on applied analysis. As a consequence of the fast pace of development, there are no textbooks that cover the full range of methods in current use and explain how to proceed in applied domains. This gap in the literature motivates the present volume. The methods are sketched out briefly to remind the reader of the ideas underlying them and to give sufficient background for empirical work. The volume can be used as a textbook for a course on applied time series econometrics. The coverage of topics follows recent methodological develop- ments. Unit root and cointegration analysis play a central part. Other topics include structural vector autoregressions, conditional heteroskedasticity, and nonlinear and nonparametric time series models. A crucial component in empirical work is the software that is available for analysis. New methodology is typically only gradually incorporated into the existing software packages. Therefore a flexible Java interface has been created that allows readers to replicate the applications and conduct their own analyses.

    Helmut Lütkepohl is Professor of Economics at the European University Institute in Florence, Italy. He is on leave from Humboldt University, Berlin, where he has been Professor of Econometrics in the Faculty of Economics and Business Administration since 1992. He had previously been Professor of Statistics at the University of Kiel (1987–92) and the University of Hamburg (1985–87) and was Visiting Assistant Professor at the University of California, San Diego (1984–85). Professor Lütkepohl is Associate Editor of Econometric Theory, the Journal of Applied Econometrics, Macroeconomic Dynamics, Empirical Economics, and Econometric Reviews. He has published extensively in learned journals and books and is author, coauthor and editor of several books on econometrics and time series analysis. Professor Lütkepohl is the author of Introduction to Multiple Time Series Analysis (1991) and a Handbook of Matrices (1996). His current teaching and research interests include methodological issues related to the study of nonstationary, integrated time series, and the analysis of the transmission mechanism of monetary policy in the euro area.

    Markus Krätzig is a doctoral student in the Department of Economics at Humboldt University, Berlin.

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    Themes in Modern Econometrics

    Managing Editor PETER C.B. PHILLIPS, Yale University

    Series Editors ERIC GHYSELS, University of North Carolina, Chapel Hill

    RICHARD J. SMITH, University of Warwick

    Themes in Modern Econometrics is designed to service the large and growing need for explicit teaching tools in econometrics. It will provide an organized sequence of textbooks in econometrics aimed squarely at the student popula- tion and will be 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 will address topics or themes that students and researchers encounter daily. Although each book will be designed to stand alone as an authoritative survey in its own right, the distinct emphasis throughout will be on pedagogic excellence.

    Titles in the Series

    Statistics and Econometric Models: Volumes 1 and 2 CHRISTIAN GOURIEROUX and ALAIN MONFORT

    Translated by QUANG VOUNG

    Time Series and Dynamic Models CHRISTIAN GOURIEROUX and ALAIN MONFORT

    Translated and edited by GIAMPIERO GALLO

    Unit Roots, Cointegration, and Structural Change G.S. MADDALA and IN-MOO KIM

    Generalized Method of Moments Estimation Edited by LÁSZLÓ MÁTYÁS

    Nonparametric Econometrics ADRIAN PAGAN and AMAN ULLAH

    Econometrics of Qualitative Dependent Variables CHRISTIAN GOURIEROUX

    Translated by PAUL B. KLASSEN

    The Econometric Analysis of Seasonal Time Series ERIC GHYSELS and DENISE R. OSBORN

    Semiparametric Regression for the Applied Econometrician ADONIS YATCHEW

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    APPLIED TIME SERIES ECONOMETRICS

    Edited by

    HELMUT LÜTKEPOHL European University Institute, Florence

    MARKUS KRÄTZIG Humboldt University, Berlin

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  • cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

    Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK

    First published in print format

    isbn-13 978-0-521-83919-8

    isbn-13 978-0-521-54787-1

    isbn-13 978-0-511-21739-5

    © Cambridge University Press 2004

    2004

    Information on this title: www.cambridge.org/9780521839198

    This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

    isbn-10 0-511-21739-0

    isbn-10 0-521-83919-x

    isbn-10 0-521-54787-3

    Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

    Published in the United States of America by Cambridge University Press, New York

    www.cambridge.org

    hardback

    paperback

    paperback

    eBook (NetLibrary)

    eBook (NetLibrary)

    hardback

    http://www.cambridge.org http://www.cambridge.org/9780521839198

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    HL To my delightful wife, Sabine

    MK To my parents

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    Contents

    Preface page xv Notation and Abbreviations xix List of Contributors xxv

    1 Initial Tasks and Overview 1 Helmut Lütkepohl

    1.1 Introduction 1 1.2 Setting Up an Econometric Project 2 1.3 Getting Data 3 1.4 Data Handling 5 1.5 Outline of Chapters 5

    2 Univariate Time Series Analysis 8 Helmut Lütkepohl

    2.1 Characteristics of Time Series 8 2.2 Stationary and Integrated Stochastic Processes 11

    2.2.1 Stationarity 11 2.2.2 Sample Autocorrelations, Partial Autocorrelations,

    and Spectral Densities 12 2.2.3 Data Transformations and Filters 17

    2.3 Some Popular Time Series Models 22 2.3.1 Autoregressive Processes 22 2.3.2 Finite-Order Moving Average Processes 25 2.3.3 ARIMA Processes 27 2.3.4 Autoregressive Conditional Heteroskedasticity 28 2.3.5 Deterministic Terms 30

    2.4 Parameter Estimation 30 2.4.1 Estimation of AR Models 30 2.4.2 Estimation of ARMA Models 32

    2.5 Model Specification 33

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    x Contents

    2.5.1 AR Order Specification Criteria 33 2.5.2 Specifying More General Models 35

    2.6 Model Checking 40 2.6.1 Descriptive Analysis of the Residuals 40 2.6.2 Diagnostic Tests of the Residuals 43 2.6.3 Stability Analysis 47

    2.7 Unit Root Tests 53 2.7.1 Augmented Dickey–Fuller (ADF) Tests 54 2.7.2 Schmidt–Phillips Tests 57 2.7.3 A Test for Processes with Level Shift 58 2.7.4 KPSS Test 63 2.7.5 Testing for Seasonal Unit Roots 65

    2.8 Forecasting Univariate Time Series 70 2.9 Examples 73

    2.9.1 German Consumption 73 2.9.2 Polish Productivity 78

    2.10 Where to Go from Here 85

    3 Vector Autoregressive and Vector Error Correction Models 86 Helmut Lütkepohl

    3.1 Introduction 86 3.2 VARs and VECMs 88

    3.2.1 The Models 88 3.2.2 Deterministic Terms 91 3.2.3 Exogenous Variables 92

    3.3 Estimation 93 3.3.1 Estimation of an Unrestricted VAR 93 3.3.2 Estimation of VECMs 96 3.3.3 Restricting the Error Correction Term 105 3.3.4 Estimation of Models with More General Restrictions

    and Structural Forms 108 3.4 Model Specification 110

    3.4.1 Determining the Autoregressive Order 110 3.4.2 Specifying the Cointegrating Rank 112 3.4.3 Choice of Deterministic Term 120 3.4.4 Testing Restrictions Related to the Cointegration

    Vectors and the Loading Matrix 121 3.4.5 Testing Restrictions for the Short-Run Parameters

    and Fitting Subset Models 122 3.5 Model Checking 125

    3.5.1 Descriptive Analysis of the Residuals 125 3.5.2 Diagnostic Tests 127 3.5.3 Stability Analysis 131

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    Contents xi

    3.6 Forecasting VAR Processes and VECMs 140 3.6.1 Known Processes 141 3.6.2 Estimated Processes 143

    3.7 Granger-Causality Analysis 144 3.7.1 The Concept 144 3.7.2 Testing for Granger-Causality 148

    3.8