Time Series Analysis With Applications in R (Springer)

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Time Series Analysis With Applications in R (Springer)
Springer Texts in Statistics Athreya Lahiri: Measure Theory and probability theory Bilodeau brenner. Theory of Multivariate Statistics Brockwell Davis: An Introduction to Time Series and Forecasting Carmona: Statistical Analysis of Financial Data in S-PLUs Chow/Teicher: Probability Theory: Independence, Interchangeability, Martingales, 3ed Christensen: Advanced Linear Modeling: Multivariate, Time Series, and Spatial Data Nonparametric Regression and Response Surface Maximization, 2 ed ls and logistic re Christensen: Plane Answers to Complex Questions: The Theory of Linear Models, 2 ed Cryer/Chan: Time Series analysis, Second edition Davis: Statistical Methods for the Analysis of Repeated Measurements Dean/Voss: Design and Analysis of Experiments Dekking/Kraaikamp/LopuhaaMeester: A Modern Introduction to Probability and Statistics urrett. essential of stochastic processes Edwards: Introduction to Graphical Modeling, 2ed Everitt: AnR and s-Plus Companion to multivariate analysis Gentle: Matrix Algebra: Theory, Computations, and Applications in Statistics Ghosh Delampady/ Samanta: An Introduction to Bayesian Analysis Gut: Probability: A Graduate Course Heiberger Holland. Statistical Analysis and Data Display; An Intermediate Course with Examples in S-PLUS.R and SAS Jobson: Applied Multivariate Data Analysis, Volume I: Regression and Experimental Design Jobson: Applied Multivariate Data Analysis, Volume Il: Categorical and Multivariate Methods Karr. Probability Kulkarni: Modeling, Analysis, Design, and Control of Stochastic Systems Lange: Applied Probability Lange: Optimization Lehmann: Elements of Large Sample Theor Lehmann/Casella: Theory of Point Estimation, 2nd ed Lehmann/Romano: Testing Statistical Hypotheses, 3 Longford. Studying Human Popluations: An Advanced Course in Statistics Marin/Robert: Bayesian Core: A Practical Approach to Computational Bayesian Statistics Nolan/Speed. Stat Labs: Mathematical Statistics Through Applications Pitman: Probability Rawlings/Pantula Dickey: Applied regression analysis Robert: The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation, 2nded Robert/Casella: monte Carlo Statistical Methods. 2ed Rose/smith Mathematical Statistics with Mathematica Ruppert: Statistics and Finance: An Introduction Sen /Srivastava: Regression Analysis: Theory, Methods, and Applications Shao: Mathematical Statistics 2n ed Shorack: Probability for Statisticians Shumway/Stoffer: Time Series Analysis and Its Applications, 2ed Simonoff: Analyzing Categorical Data Terrell: Mathematical Statistics: A Unified Introduction Timm: Applied Multivariate Analysis Toutenberg: Statistical Analysis of Designed Experiments, 2 ed Wasserman: All of Nonparametric Statistics Wasserman: All of statistics: A Concise Course in Statistical Inference Weiss: Modeling Longitudinal Data Whittle: Probability via Expectation, 4 ed Jonathan d. Cryer Kung-Sik Chan Time Series Analysis With applications in R Second edition ②Sp pringer Jonathan D. Cryer Kung-Sik Chan Department of Statistics Actuarial Science Department of Statistics Actuarial Science University of lowa University of lowa lowa City, lowa 52242 lowa City. lowa 52242 USA USA Jon-cryer(auiowaedu kung-Sik-chan auiowaedu Series editors George Casella Stephen Fienberg Ingram Okin Department of statistics Department of statistics Department of statistics University of Florida Carnegie Mellon University Stanford University Gainesville FL 32611-8545 Pittsburgh, PA 15213-3890 Stanford. CA 94305 USA USA USA ISBN:978-0-387-75958-6 e-ISBN:978-0-387-75959-3 Library of Congress Control Number: 2008923058 C2008 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 987654321 springer.com To our families PREFACE The theory and practice of time series analysis have developed rapidly since the appear- ance in 1970 of the seminal work of George E P. Box and Gwilym M. Jenkins, Time Series analysis: Forecasting and Control, now available in its third edition(1994) with co-author Gregory C. Reinsel. Many books on time series have appeared since then, but some of them give too little practical application, while others give too little theoretical background. This book attempts to present both application, and theory at a level acces sible to a wide variety of students and practitioners. Our approach is to mix application and theory throughout the book as they are naturally needed The book was developed for a one-semester course usually attended by students in statistics, economics, business, engineering, and quantitative social sciences. Basic applied statistics through multiple linear regression is assumed. Calculus is assumed only to the extent of minimizing sums of squares, but a calculus-based introduction to statistics is necessary for a thorough understanding of some of the theory. However, required facts concerning expectation, variance, covariance, and correlation are reviewed in appendices. Also, conditional expectation properties and minimum mean square error prediction are developed in appendices. Actual time series data drawn from various disciplines are used throughout the book to illustrate the methodology. The book contains additional topics of a more advanced nature that can be selected for inclusion in a course if the instructor so chooses All of the plots and numerical output displayed in the book have been produced with the r software, which is available from the r Project for Statistical Computing at www.r-project.orgSomeofthenumericaloutputhasbeeneditedforadditionalclarity or for simplicity. R is available as free software under the terms of the free Software Foundation,'s gnu general public license in source code form It runs on a wide vari- ety of uNiX platforms and similar systems, Windows, and MacOs R is a language and environment for statistical computing and graphics, provides a wide variety of statistical(e. g, time-series analysis, linear and nonlinear modeling, clas sical statistical tests) and graphical techniques, and is highly extensible. The extensive appendix An Introduction to R, provides an introduction to the r software specially designed to go with this book. One of the authors(ksC) has produced a large number of new or enhanced R functions specifically tailored to the methods described in this book They are listed on page 468 and are available in the package named tsa on the r ProjectsWebsiteatwww.r-project.orgWehavealsoconstructedrcommandscript filesforeachchapterTheseareavailablefordownloadatwww.stat.uiowa.edu/ ckchan/TSA. htm. We also show the required r code beneath nearly every table and graphical display in the book. The datasets required for the exercises are named in each exercise by an appropriate filename; for example, larain for the Los Angeles rainfall data. However, if you are using the tsa package, the datasets are part of the package and may be accessed through the r command data(larain), for example all of the datasets are also available at the textbook website as acscii files with variable names in the first row. We believe that many of the plots and calculations VIl described in the book could also be obtained with other software, such as sas, Splus Statgraphics,SCA°,EⅤiews,RATS,Ox°, and others This book is a second edition of the book Time Series Analysis by Jonathan Cryer, published in 1986 by PWs-Kent Publishing(Duxbury Press). This new edition contains nearly all of the well-received original in addition to considerable new material, numer ous new datasets, and new exercises. Some of the new topics that are integrated with the original include unit root tests, extended autocorrelation functions, subset ARIMA mod els, and bootstrapping Completely new chapters cover the topics of time series regres- sion models, time series models of heteroscedasticity, spectral analysis, and threshold models. Although the level of difficulty in these new chapters is somewhat higher than in the more basic material, we believe that the discussion is presented in a way that will make the material accessible and quite useful to a broad audience of users. Chapter 15 Threshold Models, is placed last since it is the only chapter that deals with nonlinear time series models. It could be covered earlier, say after Chapter 12. Also, Chapters 13 and 14 on spectral analysis could be covered after Chapter 10 We would like to thank John Kimmel, Executive Editor, Statistics, at Springer, for his continuing interest and guidance during the long preparation of the manuscript. Pro- fessor Howell Tong of the London School of Economics, Professor Henghsiu Tsai of Academica Sinica, Taipei, Professor Noelle Samia of Northwestern University, Profes sor W.K. Li and Professor Kai w Ng, both of the University of Hong Kong, and Profes sor Nils Christian Stenseth of the University of Oslo kindly read parts of the manuscript, and Professor Jun Yan used a preliminary version of the text for a class at the University of lowa. Their constructive comments are greatly appreciated. We would like to thank Samuel Hao who helped with the exercise solutions and read the appendix: An Introduc tion toR. We would also like to thank several anonymous reviewers who read the manu script at various stages. Their reviews led to a much improved book. Finally, one of the authors dc) would like to thank dan, Marian, and Gene for providing such a great place, Casa de Artes, Club Santiago, Mexico, for working on the first draft of much of this new edition lowa city. lowa Jonathan D. Cryer January 2008 Kung-Sik Chan CONTENTS CHAPTER 1 NTRODUCTION 1.1 EXamples of time series 1.2 A Model-Building Strategy ■口 1.3 Time Series Plots in History 1. 4 An Overview of the book 889 Exercises 10 CHAPTER 2 FUNDAMENTAL CONCEPTS 11 2.1 Time Series and stochastic Processes 2.2 Means Variances, and covariances 2.3 Stationarity 16 2.4 Summary 19 Exercises 19 Appendix A: Expectation, Variance, Covariance, and Correlation. 24 chaPteR 3 TRENDS 27 3.1 Deterministic Versus stochastic Trends .27 3.2 Estimation of a constant mean ,,,,,,,.,28 3.3 Regression Methods .30 3.4 Reliability and Efficiency of Regression Estimates 36 3.5 Interpreting Regression Output 4 3.6 Residual Analysis 42 3.7 Summary 50 Exercises 50 CHAPTER 4 MODELS FOR STATIONARY TIME SERIES 55 4.1 General Linear Processes 55 4.2 Moving average processes 57 4.3 Autoregressive Processes 66 4.4 The Mixed Autoregressive Moving Average Model 4.5 nvertibilit' 79 4.6 Summary 80 Exercises 81 Appendix B: The Stationarity Region for an AR(2) Process 84 Appendix C: The Autocorrelation Function for ARMA(p, q) .85 Contents CHAPTER 5 MODELS FOR NONSTATIONARY TIME SERIES, 87 5. 1 Stationarity Through Differencing 88 5.2 ARIMA Models ..92 5.3 Constant Terms in ARIMA Models 97 5. 4 Other Transformations 98 5.5 Summary 102 Eⅹ excises. 103 Appendix D: The Backshift Operator .106 CHAPTER 6 MODEL SPECIFICATION .109 6.1 Properties of the sample autocorrelation Function....109 6.2 The Partial and Extended Autocorrelation Functions 112 6.3 Specification of Some Simulated Time Series 6.4 Nonstationarity 125 6.5 other Specification Methods .130 6.6 Specification of Some Actual time series 133 6.7 Summary 141 Exercises ..141 CHAPTER 7 PARAMETER ESTIMATION .149 7.1 The method of moments 149 7.2 Least Squares estimation .154 7.3 Maximum Likelihood and Unconditional Least squares.. 158 7.4 Properties of the Estimates ...160 7.5 ustrations of parameter estimation .163 7.6 Bootstrapping ARIMA Models 167 7.7 Summary. 170 Exercises 170 CHAPTER 8 MODEL DIAGNOSTICS 175 8.1 Residual Analysis .175 8.2 Overfitting and Parameter Redundancy .185 83 Summary…………… 188 Eⅹ excises...,,,, ..,188 【实例截图】
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