Time Series and Dynamic Models

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Time Series and Dynamic Models Themes in Modern econometrics Managing editors PETER C.B. PHILLIPS, Yale University and ADRIAN PAGAN, Australian National University Advisory editors CHRISTIAN GOURIEROUX. CREST and CEPrEMAP Paris MICHAEL WICKENS, University of York Themes in Modern Econometrics is designed to service the large and growing need for explicit teaching tools in econometrics. It will provide an organised sequence of textbooks in econometrics aimed squarely at the student population, 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 econometrics behind them, each book will address topics or themes that students and researchers encounter daily. While each book will be designed to stand alone as an authorit- tive survey in its own right, the distinct emphasis throughout will be on pedagogic excellence Titles in the series Statistics and Econometric Models: Volume One CHRISTIAN GOURIEROUX and ALAIN MONFORT Translated by QUANG VUONG Statistics and Econometric Models: volume two CHRISTIAN GOURIEROUX and ALAIN monfort Translated by QUANG VUONG Time Series and Dynamic models CHRISTIAN GOURIEROUX and AlaIn monfort Translated and edited by GIAMPIERo M. GALLO Time series and D ynamic Models Christian Gourierou crest and CEPrEMAP. Paris Alain Monfort CREST-NSEE. Paris Translated and edited by giampiero M. Gallo CAMBRIDGE UNIVERSITY PRESS PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge CB2 IRP, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge, CB2 2RU, United Kingdom 40 West 20th Street, New York, NY 10011-421l, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Austral Originally published in French as Series Temporelles et Modeles Dynamiques by Economica 1990 ⊙Ed. ECONOMICA1990 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published in English by Cambridge University Press 1997 as Time Series and Dymamic Models English translation Cambridge University Press 1997 Typeset in 10/13 Computer Modern A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication data are available ISBN 0 521 41146 hardback IsBN 0 521 42308 2 paperback Transferred to digital printing 2003 TAG Contents Prefab Chapter 1 Introduction 1.1 Definition of a Time Series 1.2 Examples of Time Series 1.3 Graphical Representation 1.4 Some problems in Time series f the meth eo 1.6 Time-series Modeling Part I: Traditional methods Chapter 2 Linear Regression for Seasonal adjustment 19 2.1 Linear Model Setup 2.2 Uniqueness of the Decomposition 2 2.3 Transformations for the Raw seric 23 2.4 Ordinary Least sqt Estimat 25 2.5 Applications 2.6 Statistical Properties of the Estimators 28 2.7 Applications of the Regression Analysi 31 2.8 Autocorrelated Disturbances 34 2.9 Two Shortcomings of OLS 40 Contents 2. 10 An Application 41 2.11 Exercises Chapter 3 Moving Averages for easonal Adjustment 49 3.1 troduction 49 3.2 The Set of Moving Averages 5 3.3 Eigenvectors of a Moving Average 54 3.4 Transformation of a White Noise by a Moving Average 60 3.5 Arithmetic Averages 3.6 Averages Derived from the arithmetic averages 3.7 Moving Regressions 3.8 Moving Averages Derived from Minimizing the reduction ratio under Constraint 77 3.9 Distribution of the Moving Average Coefficients 3.10 Repeated Moving Averages 3.11 Treatment of the extreme points in the series 3. 12 Structural Change 3. 13 Application to the Passenger Traffic Series 92 3. 14 Appendix- Derivation of the Averages Defined in 3. 8 and 3.9 3.15 Exercises Chapter 4 Exponential Smoothing Methods 98 4.1 Simple exponential smoothi 4.2 Double Exponent Smoothing 103 4.3 The Generalized Exponential Smoothing 4.4 The holt-Winters method 45 E 115 Part II: Probabilistic and Statistical Properties of Stationary Processes Chapter 5 Some Results Univariate Processes 119 5. 1 Covariance Stationary Processes 119 52 d nd lag operators 5.3 ARMA Processes 144 5.4 ARIMA P 167 A pper 5.6 Exercises 174 Contents Chapter 6 The Box and Jenkins Method for Forecasting 179 6.1 Description of the Method 179 62 Estimation of an arima model 181 63 Identification 189 6. 4 Forecasting with ARIMA Models 197 65 Some issues 6.6 Application to the Passenger Traffic Series 208 6.7 Exercises 216 Chapter 7 Multivariate Time Series 223 7.1 Introduction 23 72 Stationary Processes 224 7.3 Linear processes 232 7.4 Appendix Representation of Matrix Sequences 238 75 Exercises 249 Chapter 8 Time-series Representations 250 8.1 ARMA Representations 250 8.2 State-space Representation 83 Frequency Domain 288 8.4 Appendix- Singular Value Decomposition Theorem 8.5 Exercises 300 Chapter 9 Estimation and Testing (Stationary Case 302 9.1 Limit Distributions of Empirical Moments 303 92 Maximum likelihood estimator 312 9.3 Testing Procedures 327 9.4 Extensions to the multivariate Case 341 95 Exercises 3 Part III: Time-series Econometrics: Stationary and Nonstationary odels Chapter 10 Causality, Exogeneity, and Shocks 355 10.1 Dynamic Macroeconometric Models 355 10.2 Causality 364 10.3卫 xogeneity 382 10.4 Shocks and multipliers 392 10.5 Appendix- Partial Links among Random Vectors 398 10.6 Exercises 408 Chapter 11 Trend Components 410 11.1 Decomposition of a series with Polynomial Trend 411


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