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淘豆网网友近日为您收集整理了关于Time Series Analysis – With Applications in R的文档，希望对您的工作和学习有所帮助。以下是文档介绍：Time Series Analysis – With Applications in R Statistics Texts in StatisticsSeries Editors:G. CasellaS. FienbergI. OlkinSpringer Texts in StatisticsAthreya/Lahiri: Measure Theory and Probability TheoryBilodeau/Brenner: Theory of Multivariate StatisticsBrockwell/Davis: An Introduction to Time Series and ForecastingCarmona: Statistical Analysis of Financial Data in S-PLUSChow/Teicher: Probability Theory: Independence, Interchangeability, Martingales, 3rded.Christensen: Advanced Linear Modeling: Mu(来源：淘豆网[/p-6381625.html])ltivariate, Time Series, and Spatial DNonparametric Regression and Response Surface Maximization, 2nded.Christensen: Log-Linear Models and Logistic Regression, 2nded.Christensen: Plane Answers plex Questions: The Theory of Linear Models, 2nded.Cryer/Chan: Time Series Analysis, Second EditionDavis: Statistical Methods for the Analysis of Repeated MeasurementsDean/Voss: Design and Analysis of ExperimentsDekking/Kraaikamp/Lopuha/Meester: A Modern I(来源：淘豆网[/p-6381625.html])ntroduction to Probability and StatisticsDurrett: Essential of Stochastic ProcessesEdwards: Introduction to Graphical Modeling, 2nded.Everitt: An R and S-panion to Multivariate AnalysisGentle: Matrix Algebra: Theory, Computations, and Applications in StatisticsGhosh/Delampady/Samanta: An Introduction to Bayesian AnalysisGut: Probability: A Graduate Coursein S-PLUS, R, and SASJobson: Applied Multivariate Data Analysis, Volume I: Regression and Experi(来源：淘豆网[/p-6381625.html])mental DesignJobson: Applied Multivariate Data Analysis, Volume II: Categorical and Multivariate MethodsKarr: ProbabilityKulkarni: Modeling, Analysis, Design, and Control of Stochastic SystemsLange: Applied ProbabilityLange: OptimizationLehmann: Elements of Large Sample TheoryLehmann/Romano: Testing Statistical Hypotheses, 3rded.Lehmann/Casella: Theory of Point Estimation, 2nded.Longford: Studying Human Popluations: An Advanced Course in StatisticsM(来源：淘豆网[/p-6381625.html])arin/Robert: Bayesian Core: A Practical Approach putational Bayesian StatisticsNolan/Speed: Stat Labs: Mathematical Statistics Through ApplicationsPitman: ProbabilityRawlings/Pantula/Dickey: Applied Regression AnalysisRobert: The Bayesian Choice: From Decision-Theoretic Foundations putationalImplementation, 2nded.Robert/Casella: Monte Carlo Statistical Methods, 2nded.Rose/Smith: Mathematical Statistics with MathematicaRuppert: Statistics and Finance(来源：淘豆网[/p-6381625.html]): An IntroductionSen/Srivastava: Regression Analysis: Theory, Methods, and Applications.Shao: Mathematical Statistics, 2nded.Shorack: Probability for StatisticiansShumway/Stoffer: Time Series Analysis and Its Applications, 2nded.Simonoff: Analyzing Categorical DataTerrell: Mathematical Statistics: A Unified IntroductionTimm: Applied Multivariate AnalysisToutenberg: Statistical Analysis of Designed Experiments, 2nded.Wasserman: All of Nonparametric S(来源：淘豆网[/p-6381625.html])tatisticsWasserman: All of Statistics: A Concise Course in Statistical InferenceWeiss: Modeling Longitudinal DataWhittle: Probability via Expectation, 4thed.Heiberger/Holland: Statistical Analysis and Data D An Intermediate Course with ExamplesTime Series AnalysisJonathan D. Cryer
Kung-Sik ChanWith Applications in RSecond e CasellaUniversity of FloridaUSADepartment of StatisticsCarnegie Mellon UniversityUSAPittsburgh, PA Ingram Oki(来源：淘豆网[/p-6381625.html])nDepartment of StatisticsStanford, CA 94305USASeries Editors:Department of StatisticsISBN: 978-0-387- Springer Science+Business Media, LLCPrinted on acid-free paper.9 8 7 6 5 4 3 2 Stephen FienbergStanford Universitye-ISBN: 978-0-387-75959-3All rights reserved. This work may not be translated or copied in whole or in part without the written permissionof the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY (来源：淘豆网[/p-6381625.html])10013, USA),except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with anyform of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology 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 notidentified as such, is not to be taken as an expression of (来源：淘豆网[/p-6381625.html])opinion as to whether or not they are subject toproprietary rights.Library of Congress Control Number: Gainesville, FL Jonathan D. CryerDepartment of Statistics & Actuarial ScienceUniversity of IowaIowa City, Iowa 52242USAjon-cryer@uiowa.eduKung-Sik ChanDepartment of Statistics & Actuarial ScienceUniversity of IowaIowa City, Iowa 52242USAkung-sik-chan@uiowa.eduTo our familiesviiPREFACEThe theory and practice of time serie(来源：淘豆网[/p-6381625.html])s analysis have developed rapidly since the appear-ance in 1970 of the seminal work of e E. P. Box and Gwilym M. Jenkins, TimeSeries Analysis: Forecasting and Control, now available in its third edition (1994) withco-author Gregory C. Reinsel. Many books on time series have appeared since then, butsome of them give too little practical application, while others give too little theoreticalbackground. 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 applicationand theory throughout the book as they are naturally needed.The book was developed for a one-semester course usually attended by students instatistics, economics, business, engineering, and quantitative social sciences. Basicapplied statistics through multiple linear regression is assumed. Calculus is assumedonly to the extent of minimizing sums of squares, but a calculus-based introduction tostatistics is necessary for a thorough understanding of some of the theory. However,required facts concerning expectation, variance, covariance, and correlation arereviewed in appendices. Also, conditional expectation properties and minimum meansquare error prediction are developed in appendices. Actual time series data drawn fromvarious disciplines are used throughout the book to illustrate the methodology. The bookcontains additional topics of a more advanced nature that can be selected for inclusion ina course if the instructor so chooses.All of the plots and numerical output displayed in the book have been producedwith the R software, which is available from the R Project for puting . Some of the numerical output has been edited for additional clarityor for simplicity. R is available as free software under the terms of the Free SoftwareFoundation'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 puting and graphics, provides awide variety of statistical (e.g., time-series analysis, linear and nonlinear modeling, clas-sical statistical tests) and graphical techniques, and is highly extensible. The extensiveappendix An Introduction to R, provides an introduction to the R software speciallydesigned to go with this book. One of the authors (KSC) has produced a large number ofnew 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 RProject’s Website at .org. We have also constructed mand scriptfiles for each chapter. These are available for download at .edu/~kchan/TSA.htm. We also show the required R code beneath nearly every table andgraphical display in the book. The datasets required for the exercises are named in eachexercise by an
for example, larain for the Los Angeles rainfalldata. However, if you are using the TSA package, the datasets are part of the packageand may be accessed through the mand data(larain), for example.All of the datasets are also available at the textbook website as ACSCII files withvariable names in the first row. We believe that many of the plots and calculationsdescribed 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 containsnearly 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 theoriginal 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 thresholdmodels. Although the level of difficulty in these new chapters is somewhat higher thanin the more basic material, we believe that the discussion is presented in a way that willmake 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 nonlineartime series models. It could be covered earlier, say after Chapter 12. Also, Chapters 13and 14 on spectral analysis could be covered after Chapter 10.We would like to thank John Kimmel, Executive Editor, Statistics, at Springer, forhis continuing interest and guidance during the long preparation of the manuscript. Pro-fessor Howell Tong of the London School of Economics, Professor Henghsiu Tsai ofAcademica 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 Universityof Iowa. Their ments are greatly appreciated. We would like to thankSamuel Hao who helped with the exercise solutions and read the appendix: An Introduc-tion to R. 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 theauthors (JDC) would like to thank Dan, Marian, and Gene for providing such a greatplace, Casa de Artes, Club Santiago, Mexico, for working on the first draft of much ofthis new edition.Iowa City, Iowa Jonathan D. CryerJanuary 2008 Kung-Sik ChanixCONTENTSCHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Examples of Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 A Model-Building Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 Time Series Plots in History . . . . . . . . . . . . . . . . . . . . . . . . . . 81.4 An Overview of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10CHAPTER 2 FUNDAMENTAL CONCEPTS . . . . . . . . . . . . . . . . . . 112.1 Time Series and Stochastic Processes . . . . . . . . . . . . . . . . 112.2 Means, Variances, and Covariances . . . . . . . . . . . . . . . . . . 112.3 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Appendix A: Expectation, Variance, Covariance, and Correlation . 24CHAPTER 3 TRENDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.1 Deterministic Versus Stochastic Trends . . . . . . . . . . . . . . . . 273.2 Estimation of a Constant Mean . . . . . . . . . . . . . . . . . . . . . . 283.3 Regression Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.4 Reliability and Efficiency of Regression Estimates. . . . . . . . 363.5 Interpreting Regression Output . . . . . . . . . . . . . . . . . . . . . . 403.6 Residual Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50CHAPTER 4 MODELS FOR STATIONARY TIME SERIES. . . . . 554.1 General Linear Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 554.2 Moving Average Processes . . . . . . . . . . . . . . . . . . . . . . . . . 574.3 Autoregressive Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 664.4 The Mixed Autoregressive Moving Average Model. . . . . . . . 774.5 Invertibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Appendix B: The Stationarity Region for an AR(2) Process . . . . . 84Appendix C: The Autocorrelation Function for ARMA(p,q). . . . . . . 85CHAPTER 5 MODELS FOR NONSTATIONARY TIME SERIES .875.1 Stationarity Through Differencing . . . . . . . . . . . . . . . . . . . . .885.2 ARIMA Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .925.3 Constant Terms in ARIMA Models. . . . . . . . . . . . . . . . . . . . .975.4 Other Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .985.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103Appendix D: The Backshift Operator. . . . . . . . . . . . . . . . . . . . . . .106CHAPTER 6 MODEL SPECIFICATION. . . . . . . . . . . . . . . . . . . . .1096.1 Properties of the Sample Autocorrelation Function . . . . . . .1096.2 The Partial and Extended Autocorrelation Functions . . . . .1126.3 Specification of Some Simulated Time Series. . . . . . . . . . .1176.4 Nonstationarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1256.5 Other Specification Methods . . . . . . . . . . . . . . . . . . . . . . . .1306.6 Specification of Some Actual Time Series. . . . . . . . . . . . . .1336.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141CHAPTER 7 PARAMETER ESTIMATION . . . . . . . . . . . . . . . . . . .1497.1 The Method of Moments . . . . . . . . . . . . . . . . . . . . . . . . . . .1497.2 Least Squares Estimation . . . . . . . . . . . . . . . . . . . . . . . . . .1547.3 Maximum Likelihood and Unconditional Least Squares . . .1587.4 Properties of the Estimates . . . . . . . . . . . . . . . . . . . . . . . . .1607.5 Illustrations of Parameter Estimation . . . . . . . . . . . . . . . . . .1637.6 Bootstrapping ARIMA Models . . . . . . . . . . . . . . . . . . . . . . .1677.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170CHAPTER 8 MODEL DIAGNOSTICS . . . . . . . . . . . . . . . . . . . . . .1758.1 Residual Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1758.2 Overfitting and Parameter Redundancy. . . . . . . . . . . . . . . .1858.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .188Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .188播放器加载中，请稍候...
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Time Series Analysis – With Applications in R Statistics Texts in StatisticsSeries Editors:G. CasellaS. FienbergI. OlkinSpringer Texts in StatisticsAthreya/Lahiri: Measure Theory and Probability TheoryBilodeau/Brenner: Theory of Multivariate StatisticsBrockwell/Davis: An Introduction to Time Series...
内容来自淘豆网转载请标明出处.AR(1) Model
Autoregressive Time Series Modeling
This site is a part of the JavaScript
learning objects for decision making.
Other JavaScript in this series are categorized under different areas of applications in the
section on this page.
This site provides the necessary tools for the identification, estimation, and forecasting based on autoregressive order one obtained from a given time series:
F1X(t) + et,
where et is a White-Noise series.
Note that, the
Stationary Condition: | F1| & 1
is expressed as a null hypothesis H0 and being tested.
Notice: As always, it is necessary to construct the
and , compute
and check for both
in mean and variance, as well as the
For many time-series one must perform, and/or
prior to using this JavaScript.
Enter your up-to-84, ordered values of your time series, row-wise and, then click the Calculate button.
Blank boxes are not included in the calculations but zeros are.
In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.
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Autorrelation
Standard Error
Standard Error
Standard Error
Stationary Condition: | F1|
White Noise Analysis and Diagnostic Tools
The first half
The second half
The first-half
The second half
order serial-correlation
order serial-correlation
First partial serial-correlation
Second partial serial-correlation
Durbin-Watson
Mean absolute
Normality Condition
White Noise
ith Step Ahead Forecast
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