Time Series Analysis: Forecasting and Control / Edition 4

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This is a revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application -forecasting, model specification, estimation, modeling the effects of intervention events, and process control, among others. In addition to meticulous modifications in content and improvements in style, the new edition 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.

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Editorial Reviews

From the Publisher
'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)

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Product Details

Meet the Author

George E. P. Box, PHD, is Ronald Aylmer Fisher Professor Emeritus of Statistics at the University of Wisconsin-Madison. He is a Fellow of the American Academy of Arts and Sciences and a recipient of the Samuel S. Wilks Memorial Medal of the American Statistical Association, the Shewhart Medal of the American Society for Quality, and the Guy Medal in Gold of the Royal Statistical Society. Dr. Box is the coauthor of Statistics for Experimenters: Design, Innovation, and Discovery, Second Edition; Response Surfaces, Mixtures, and Ridge Analyses, Second Edition; Evolutionary Operation: A Statistical Method for Process Improvement; Statistical Control: By Monitoring and Feedback Adjustment; and Improving Almost Anything: Ideas and Essays, Revised Edition, all published by Wiley.

The late Gwilym M. Jenkins, PHD, was professor of systems engineering at Lancaster University in the United Kingdom, where he was also founder and managing director of the International Systems Corporation of Lancaster? A Fellow of the Institute of Mathematical Statistics and the Institute of Statisticians, Dr. Jenkins had a prestigious career in both academia and consulting work that included positions at Imperial College London, Stanford University,Princeton University, and the University of Wisconsin-Madison. He was widely known for his work on time series analysis, most notably his groundbreaking work with Dr. Box on the Box-Jenkins models.

The late Gregory CD. Reinsel, PHD, was professor and former chair of the department of Statistics at the University of Wisconsin-Madison. Dr. Reinsel's expertise was focused on time series analysis and its applications in areas as diverse as economics, ecology, engineering, and meteorology. He authored over seventy refereed articles and three books, and was a Fellow of both the American Statistical Association and the Institute of Mathematical Statistics.

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Table of Contents

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

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