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Time Series Analysis: Forecasting and Control, 4th Edition

Time Series Analysis: Forecasting and Control, 4th Edition

George E. P. Box, Gwilym M. Jenkins, Gregory C. Reinsel

ISBN: 978-0-470-27284-8

Jun 2008

784 pages


A modernized new edition of one of the most trusted books on time series analysis. Since publication of the first edition in 1970, Time Series Analysis has served as one of the most influential and prominent works on the subject. This new edition maintains its balanced presentation of the tools for modeling and analyzing time series and also introduces the latest developments that have occurred n the field over the past decade through applications from areas such as business, finance, and engineering.

The Fourth Edition provides a clearly written exploration of the key methods for building, classifying, testing, and analyzing stochastic models for time series as well as their use in five important areas of application: forecasting; determining the transfer function of a system; modeling the effects of intervention events; developing multivariate dynamic models; and designing simple control schemes. Along with these classical uses, modern topics are introduced through the book's new features, which include:

  • A new chapter on multivariate time series analysis, including a discussion of the challenge that arise with their modeling and an outline of the necessary analytical tools
  • New coverage of forecasting in the design of feedback and feedforward control schemes
  • A new chapter on nonlinear and long memory models, which explores additional models for application such as heteroscedastic time series, nonlinear time series models, and models for long memory processes
  • Coverage of structural component models for the modeling, forecasting, and seasonal adjustment of time series
  • A review of the maximum likelihood estimation for ARMA models with missing values

Numerous illustrations and detailed appendices supplement the book,while extensive references and discussion questions at the end of each chapter facilitate an in-depth understanding of both time-tested and modern concepts. With its focus on practical, rather than heavily mathematical, techniques, Time Series Analysis, Fourth Edition is the upper-undergraduate and graduate levels. this book is also an invaluable reference for applied statisticians, engineers, and financial analysts.

Preface to the Fourth Edition xxi

Preface to the Third Edition xxiii

1 Introduction 1

1.1 Five Important Practical Problems, 2

1.2 Stochastic and Deterministic Dynamic Mathematical Models, 7

1.3 Basic Ideas in Model Building, 16

Part One Stochastic Models and Their Forecasting 19

2 Autocorrelation Function and Spectrum of Stationary Processes 21

2.1 Autocorrelation Properties of Stationary Models, 21

2.2 Spectral Properties of Stationary Models, 35

3 Linear Stationary Models 47

3.1 General Linear Process, 47

3.2 Autoregressive Processes, 55

3.3 Moving Average Processes, 71

3.4 Mixed Autoregressive–Moving Average Processes, 79

4 Linear Nonstationary Models 93

4.1 Autoregressive Integrated Moving Average Processes, 93

4.2 Three Explicit Forms for The Autoregressive Integrated Moving Average Model, 103

4.3 Integrated Moving Average Processes, 114

5 Forecasting 137

5.1 Minimum Mean Square Error Forecasts and Their Properties, 137

5.2 Calculating and Updating Forecasts, 145

5.3 Forecast Function and Forecast Weights, 152

5.4 Examples of Forecast Functions and Their Updating, 157

5.5 Use of State-Space Model Formulation for Exact Forecasting, 170

5.6 Summary, 177

Part Two Stochastic Model Building 193

6 Model Identification 195

6.1 Objectives of Identification, 195

6.2 Identification Techniques, 196

6.3 Initial Estimates for the Parameters, 213

6.4 Model Multiplicity, 221

7 Model Estimation 231

7.1 Study of the Likelihood and Sum-of-Squares Functions, 231

7.2 Nonlinear Estimation, 255

7.3 Some Estimation Results for Specific Models, 268

7.4 Likelihood Function Based on the State-Space Model, 275

7.5 Unit Roots in Arima Models, 280

7.6 Estimation Using Bayes’s Theorem, 287

8 Model Diagnostic Checking 333

8.1 Checking the Stochastic Model, 333

8.2 Diagnostic Checks Applied to Residuals, 335

8.3 Use of Residuals to Modify the Model, 350

9 Seasonal Models 353

9.1 Parsimonious Models for Seasonal Time Series, 353

9.2 Representation of the Airline Data by a Multiplicative (0, 1, 1) × (0, 1, 1)12 Model, 359

9.3 Some Aspects of More General Seasonal ARIMA Models, 375

9.4 Structural Component Models and Deterministic Seasonal Components, 384

9.5 Regression Models with Time Series Error Terms, 397

10 Nonlinear and Long Memory Models 413

10.1 Autoregressive Conditional Heteroscedastic (ARCH) Models, 413

10.2 Nonlinear Time Series Models, 420

10.3 Long Memory Time Series Processes, 428

Part Three Transfer Function and Multivariate Model Building 437

11 Transfer Function Models 439

11.1 Linear Transfer Function Models, 439

11.2 Discrete Dynamic Models Represented by Difference Equations, 447

11.3 Relation Between Discrete and Continuous Models, 458

12 Identification, Fitting, and Checking of Transfer Function Models 473

12.1 Cross-Correlation Function, 474

12.2 Identification of Transfer Function Models, 481

12.3 Fitting and Checking Transfer Function Models, 492

12.4 Some Examples of Fitting and Checking Transfer Function Models, 501

12.5 Forecasting With Transfer Function Models Using Leading Indicators, 509

12.6 Some Aspects of the Design of Experiments to Estimate Transfer Functions, 519

13 Intervention Analysis Models and Outlier Detection 529

13.1 Intervention Analysis Methods, 529

13.2 Outlier Analysis for Time Series, 536

13.3 Estimation for ARMA Models with Missing Values, 543

14 Multivariate Time Series Analysis 551

14.1 Stationary Multivariate Time Series, 552

14.2 Linear Model Representations for Stationary Multivariate Processes, 556

14.3 Nonstationary Vector Autoregressive–Moving Average Models, 570

14.4 Forecasting for Vector Autoregressive–Moving Average Processes, 573

14.5 State-Space Form of the Vector ARMA Model, 575

14.6 Statistical Analysis of Vector ARMA Models, 578

14.7 Example of Vector ARMA Modeling, 588

Part Four Design of Discrete Control Schemes 597

15 Aspects of Process Control 599

15.1 Process Monitoring and Process Adjustment, 600

15.2 Process Adjustment Using Feedback Control, 604

15.3 Excessive Adjustment Sometimes Required by MMSE Control, 620

15.4 Minimum Cost Control with Fixed Costs of Adjustment and Monitoring, 623

15.5 Feedforward Control, 627

15.6 Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes, 642

Part Five Charts and Tables 659

Collection of Tables and Charts 661

Collection of Time Series Used for Examples in the Text and in Exercises 669

References 685

Part Six Exercises and Problems 701

Index 729

  • While preserving the general overall structure of the original book, several revisions, modifications, and omissions of text have been made to strengthen the understanding.
  • The control section of the book has been reworked to reflect the increasing roles of process monitoring and process adjustment. 
  • New edition now includes coverage of multivariate statistics, with a new chapter devoted to multivariate time series analysis 
  • Incorporates several new topics in an effort to modernize the subject matter. These topics include extensive discussions of multivariate time series, smoothing, likelihood function based on the state space model, autoregressive models, structural component models and deterministic seasonal components, and nonlinear and long memory models.


?The book follows faithfully the style of the original edition. The approach is heavily motivated by real world time series, and by developing a complete approach to model building, estimation, forecasting and control.? (Mathematical Reviews, 2009)

"I think the book is very valuable and useful to graduate students in statistics, mathematics, engineering, and the like. Also, it could be of tremendous help to practioners. Even though the book is written in a clear, easy to follow narrative style with plenty of illustrations, one should nevertheless have a sufficient knowledge of graduate level mathematical statistics. By reading and understanding the book one should, in the end, feel very confident in time series and analysis." (MAA Reviews, January 13, 2009)

"I think the book is very valuable and useful to graduate students in statistics, mathematics, engineering, and the like.  Also, it could be of tremendous help to practioners.  Even though the book is written in a clear, easy to follow narrative style with plenty of illustrations, one should nevertheless have a sufficient knowledge of graduate level mathematical statistics.  By reading and understanding the book one should, in the end, feel very confident in time series and analysis." (MAA Reviews, January 2009)

  • The book is lavishly displayed with graphics, exercise sets, and real-life examples from areas of study such as economics, business, engineering, and the natural sciences. 
  • Chapter appendices present more demanding material that can otherwise be skipped without loss of continuity.
  • Extensive references provide ample content for further study. 
  • Every engineering, financial analyst, and applied statistician should have a copy of this invaluable guide.