Analysis of Integrated and Cointegrated Time Series with R PDF
Preview Analysis of Integrated and Cointegrated Time Series with R
Use R! Series Editors: Robert Gentleman Kurt Hornik Giovanni Parmigiani Use R! Albert: Bayesian Computation with R Bivand/Pebesma/Gómez-Rubio: Applied Spatial Data Analysis with R Claude: Morphometrics with R Cook: Interactive andDynamic Graphics for Data Analysis Hahne/Huber/Gentleman/Falcon:Bioconductor Case Studies Nason: Wavelet Methods in Statistics with R Paradis: Analysis of Phylogenetics and Evolution with R Peng/Dominici: Statistical Methods for Environmental Epidemiology with R Pfaff: Analysis ofIntegrated and Cointegrated Time Series with R Sarkar: Lattice: MultivariateData Visualization with R Spector:Data Manipulation with R Bernhard Pfaff Analysis of Integrated and Cointegrated Time Series with R Dr. Bernhard Pfaff 61476 Kronberg im Taunus Germany Series Editors: Robert Gentleman Kurt Hornik Program in Computational Biology Department für Statistik und Mathematik Division ofPublic Health Sciences Wirtschaftsuniversität Wien Augasse 2-6 Fred Hutchinson Cancer Research Center A-1090 Wien 1100 Fairview Ave.N,M2-B876 Austria Seattle,Washington981029-1024 USA Giovanni Parmigiani The Sidney Kimmel Comprehensive Cancer Center at Johns Hopkins University 550 North Broadway Baltimore,MD21205-2011 USA ISBN 978-0-387-75966-1 e-ISBN 978-0-387-75967-8 Library of Congress Control Number: 2008930126 ©2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com To my parents Preface to the Second Edition A little more than two years have passed since the first edition. During this time, R has gainedfurther groundin the domainofeconometrics.This is wit- nessed by the 2006 useR! conference in Vienna, where many sessions were devoted entirely to econometric topics, as well as the Rmetrics workshop at Meielisalp2007.AforthcomingspecialissueoftheJournal of Statistical Soft- ware will be devoted entirely to econometric methods that have been imple- mentedwithinR.Furthermore,numerousnewpackageshavebeencontributed to CRAN and existing ones have been improved; a total of more than 1200 arenowavailable.To keepupwiththese pleasantchanges,itis thereforenec- essary not only to adjust the R code examples from the first edition but also to enlarge the book’s content with new topics. However, the book’s skeleton and intention stays unchanged, given the positive feedback received from instructors and users alike. Compared with the first edition, vector autoregressive (VARs) models and structural vector autoregressive (SVARs) models have been included in an entire new chapter in the first part of the book. The theoretical underpinnings, definitions, and motivation of VAR and SVAR models are outlined, and the various methods thatareappliedtothesekindsofmodelsareillustratedbyartificialdatasets. Inparticular,itisshownhowswiftlydifferentestimationprinciples,inference, diagnostic testing, impulse response analysis, forecast error variance decom- position, and forecasting can be conducted with R. Thereby the gap to vec- tor error-correction models (VECMs) and structural vector error-correction (SVEC)modelsisbridged.Theformermodelsarenowintroducedmorethor- oughly in the last chapter of the first part, and an encompassing analysis in the context of VEC/SVEC modeling is presented in the book’s last chapter. As was the case for the first edition, all R code examples presented can be downloaded from http://www.pfaffikus.de. As with the first edition, I would like to thank the R Core Team for providing such a superb piece of software to the public and to the numerous packageauthorswhohaveenrichedthissoftwareenvironment.Iwouldfurther like to express my gratitude to the anonymous referees who have given good viii Preface totheSecond Edition pointers for improvingthis secondedition. Of course,allremaining errorsare mine. Last but not least, I would like to thank my editor, John Kimmel, for his continuous encouragementand support. Kronberg im Taunus Bernhard Pfaff March 2008 Preface This book’s title is the synthesis of two influential and outstanding entities. To quote David Hendry in the Nobel Memorial Prize lecture for Clive W. J.Granger,“[the]modelingofnon-stationarymacroeconomictime series[...] hasnowbecomethedominantparadigminempiricalmacroeconomicresearch” (Hendry[2004]).Hence,athoroughcommandofintegrationandcointegration analysis is a must for the applied econometrician. On the other side is the open-source statistical programming environment R. Since the mid-1990s, it hasgrownsteadilyoutofinfancyandcannowbe consideredmature,flexible, and powerful software with more than 600 contributed packages. However,it is fairto saythatR hasnotyetreceivedthe attentionamongeconometricians it deserves. This book tries to bridge this gap by showing how easily the methods and tools encountered in integration and cointegration analysis are implemented in R. Thisbookaddressesseniorundergraduateandgraduatestudentsandprac- titionersalike.Althoughthebook’scontentisnotapuretheoreticalexposition ofintegrationandcointegrationanalysis,itisparticularlysuitedasanaccom- panyingtextinappliedcomputerlaboratoryclasses.Wherepossible,thedata setsoftheoriginalarticleshavebeenusedintheexamplessuchthatthereader can work through them step by step and thereby replicate the results. Exer- cisesareincludedaftereachchapter.Theseexercisesarewrittenwiththeaim offosteringthe reader’scommandof Randapplyingthe previouslypresented tests and methods.It is assumedthat the readerhas alreadygainedsome ex- perience with R by working through the relevant chapters in Dalgaard [2002] andVenablesandRipley[2002]aswellasthemanual“AnIntroductiontoR.” Thisbookisdividedintothreeparts.Inthefirstpart,theoreticalconcepts of time series analysis, unit root processes, and cointegration are presented. Although the book’s aim is not a thorough theoretical exposition of these methods,this firstpartservesasa unifying introductiontothe notationused and as a brief refresher of the theoretical underpinnings of the practical ex- amples in the later chapters. The focus of the second part is the testing of the unit root hypothesis. The common testing procedure of the augmented x Preface Dickey-Fuller test for detecting the order of integrationis considered first. In the later sections, other unit root tests encountered widely in applied econo- metrics, such as the Phillips-Perron,Elliott-Rothenberg-Stock,Kwiatkowski- Phillips-Schmidt-Shin,andSchmidt-Phillipstests,arepresented,aswellasthe case of seasonalunit rootsand processesthat are contaminatedby structural shifts. The topic of the third and last part is cointegration. As an introduc- tion,the two-stepmethodofEngleandGrangerandthemethodproposedby Phillips and Ouliaris are discussed before finally Johansen’s method is pre- sented. The book ends with an exposition of vector error-correction models that are affected by a one-time structural shift. At this point, I would like to express my gratitude to the R Core Team for making this softwareavailable to the public and to the numerous package authorswhohaveenrichedthissoftwareenvironment.Theanonymousreferees are owed a special thanks for the suggestions made. Of course, all remaining errors are mine. Last but not least, I would like to thank my editor, John Kimmel, for his continuous encouragementand support. Kronberg im Taunus Bernhard Pfaff September 2005 Contents Preface to the Second Edition ................................. vii Preface ........................................................ ix List of Tables.................................................. xv List of Figures.................................................xvii List of R Code ................................................. xix Part I Theoretical Concepts 1 Univariate Analysis of Stationary Time Series ............. 3 1.1 Characteristics of Time Series............................. 3 1.2 AR(p) Time Series Process ............................... 6 1.3 MA(q) Time Series Process ............................... 10 1.4 ARMA(p, q) Time Series Process.......................... 14 Summary ................................................... 20 Exercises ................................................... 21 2 Multivariate Analysis of Stationary Time Series ........... 23 2.1 Overview............................................... 23 2.2 Vector AutoregressiveModels ............................. 23 2.2.1 Specification, Assumptions, and Estimation........... 23 2.2.2 Diagnostic Tests .................................. 28 2.2.3 Causality Analysis................................. 34 2.2.4 Forecasting ....................................... 36 2.2.5 Impulse Response Functions ....................... 37 2.2.6 Forecast Error Variance Decomposition .............. 41 2.3 Structural Vector Autoregressive Models ................... 43 2.3.1 Specification and Assumptions ...................... 43
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