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Time series analysis: forecasting and control

Time series analysis: forecasting and control

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

Focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject, this work explores the building of stochastic (statistical) models for time series and their use in important areas of application - forecasting, model specification and estimation, among others

Book. English.
4th ed.
Published Oxford: Wiley-Blackwell, 2008
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Details

Statement of responsibility: George E.P. Box, Gwilym M. Jenkins, Gregory C. Reinsel
ISBN: 0470272848, 9780470272848
Intended audience: Specialized.
Note: Previous ed.: Englewood Cliffs, N.J.: Prentice Hall, 1994.
Note: Includes index.
Physical Description: 776 p.
Series: Wiley series in probability and statistics
Subject: Time-series analysis.; Transfer functions.; Feedback control systems Mathematical models.; Prediction theory.

Contents

  1. Preface to the Fourth Edition xxi
  2. Preface to the Third Edition xxiii
  3. 1 Introduction
  4. 1.1 Five Important Practical Problems
  5. 1.2 Stochastic and Deterministic Dynamic Mathematical Models,7
  6. 1.3 Basic Ideas in Model Building
  7. Part One Stochastic Models and Their Forecasting
  8. 2 Autocorrelation Function and Spectrum of StationaryProcesses
  9. 2.1 Autocorrelation Properties of Stationary Models
  10. 2.2 Spectral Properties of Stationary Models
  11. 3 Linear Stationary Models
  12. 3.1 General Linear Process
  13. 3.2 Autoregressive Processes
  14. 3.3 Moving Average Processes
  15. 3.4 Mixed Autoregressive Moving Average Processes
  16. 4 Linear Nonstationary Models
  17. 4.1 Autoregressive Integrated Moving Average Processes
  18. 4.2 Three Explicit Forms for The Autoregressive IntegratedMoving Average Model
  19. 4.3 Integrated Moving Average Processes
  20. 5 Forecasting
  21. 5.1 Minimum Mean Square Error Forecasts and Their Properties,137
  22. 5.2 Calculating and Updating Forecasts
  23. 5.3 Forecast Function and Forecast Weights
  24. 5.4 Examples of Forecast Functions and Their Updating
  25. 5.5 Use of State–Space Model Formulation for Exact Forecasting,170
  26. 5.6 Summary
  27. Part Two Stochastic Model Building
  28. 6 Model Identification
  29. 6.1 Objectives of Identification
  30. 6.2 Identification Techniques
  31. 6.3 Initial Estimates for the Parameters
  32. 6.4 Model Multiplicity
  33. 7 Model Estimation
  34. 7.1 Study of the Likelihood and Sum–of–Squares Functions,231
  35. 7.2 Nonlinear Estimation
  36. 7.3 Some Estimation Results for Specific Models
  37. 7.4 Likelihood Function Based on the State–Space Model
  38. 7.5 Unit Roots in Arima Models
  39. 7.6 Estimation Using Bayes s Theorem
  40. 8 Model Diagnostic Checking
  41. 8.1 Checking the Stochastic Model
  42. 8.2 Diagnostic Checks Applied to Residuals
  43. 8.3 Use of Residuals to Modify the Model
  44. 9 Seasonal Models
  45. 9.1 Parsimonious Models for Seasonal Time Series
  46. 9.2 Representation of the Airline Data by a Multiplicative (0,1, 1) × (0, 1, 1)12 Model
  47. 9.3 Some Aspects of More General Seasonal ARIMA Models
  48. 9.4 Structural Component Models and Deterministic SeasonalComponents
  49. 9.5 Regression Models with Time Series Error Terms
  50. 10 Nonlinear and Long Memory Models
  51. 10.1 Autoregressive Conditional Heteroscedastic (ARCH) Models,413
  52. 10.2 Nonlinear Time Series Models
  53. 10.3 Long Memory Time Series Processes
  54. Part Three Transfer Function and Multivariate Model Building437
  55. 11 Transfer Function Models
  56. 11.1 Linear Transfer Function Models
  57. 11.2 Discrete Dynamic Models Represented by DifferenceEquations
  58. 11.3 Relation Between Discrete and Continuous Models
  59. 12 Identification, Fitting, and Checking of Transfer FunctionModels
  60. 12.1 Cross–Correlation Function
  61. 12.2 Identification of Transfer Function Models
  62. 12.3 Fitting and Checking Transfer Function Models
  63. 12.4 Some Examples of Fitting and Checking Transfer FunctionModels
  64. 12.5 Forecasting With Transfer Function Models Using LeadingIndicators
  65. 12.6 Some Aspects of the Design of Experiments to EstimateTransfer Functions
  66. 13 Intervention Analysis Models and Outlier Detection529
  67. 13.1 Intervention Analysis Methods
  68. 13.2 Outlier Analysis for Time Series
  69. 13.3 Estimation for ARMA Models with Missing Values
  70. 14 Multivariate Time Series Analysis
  71. 14.1 Stationary Multivariate Time Series
  72. 14.2 Linear Model Representations for Stationary MultivariateProcesses
  73. 14.3 Nonstationary Vector Autoregressive Moving AverageModels
  74. 14.4 Forecasting for Vector Autoregressive Moving AverageProcesses
  75. 14.5 State–Space Form of the Vector ARMA Model
  76. 14.6 Statistical Analysis of Vector ARMA Models
  77. 14.7 Example of Vector ARMA Modeling
  78. Part Four Design of Discrete Control Schemes
  79. 15 Aspects of Process Control
  80. 15.1 Process Monitoring and Process Adjustment
  81. 15.2 Process Adjustment Using Feedback Control
  82. 15.3 Excessive Adjustment Sometimes Required by MMSE Control,620
  83. 15.4 Minimum Cost Control with Fixed Costs of Adjustment andMonitoring
  84. 15.5 Feedforward Control
  85. 15.6 Monitoring Values of Parameters of Forecasting and FeedbackAdjustment Schemes
  86. Part Five Charts and Tables
  87. Collection of Tables and Charts
  88. Collection of Time Series Used for Examples in the Text and inExercises
  89. References
  90. Part Six Exercises and Problems
  91. Index

Author note

George E. P. Box, PHD, is Ronald Aylmer Fisher ProfessorEmeritus of Statistics at the University of Wisconsin–Madison. Heis a Fellow of the American Academy of Arts and Sciences and arecipient of the Samuel S. Wilks Memorial Medal of the AmericanStatistical Association, the Shewhart Medal of the American Societyfor Quality, and the Guy Medal in Gold of the Royal StatisticalSociety. Dr. Box is the coauthor of Statistics for Experimenters:Design, Innovation, and Discovery, Second Edition; ResponseSurfaces, Mixtures, and Ridge Analyses, Second Edition;Evolutionary Operation: A Statistical Method for ProcessImprovement; Statistical Control: By Monitoring and FeedbackAdjustment; and Improving Almost Anything: Ideas and Essays,Revised Edition, all published by Wiley.

The late Gwilym M. Jenkins, PHD, was professor of systemsengineering at Lancaster University in the United Kingdom, where hewas also founder and managing director of the International SystemsCorporation of Lancaster? A Fellow of the Institute of MathematicalStatistics and the Institute of Statisticians, Dr. Jenkins had aprestigious career in both academia and consulting work thatincluded positions at Imperial College London, StanfordUniversity,Princeton University, and the University ofWisconsin–Madison. He was widely known for his work on time seriesanalysis, most notably his groundbreaking work with Dr. Box on theBox–Jenkins models.

The late Gregory CD. Reinsel, PHD, was professor andformer chair of the department of Statistics at the University ofWisconsin–Madison. Dr. Reinsel′s expertise was focused on timeseries analysis and its applications in areas as diverse aseconomics, ecology, engineering, and meteorology. He authored overseventy refereed articles and three books, and was a Fellow of boththe American Statistical Association and the Institute ofMathematical Statistics.

Description

A modernized new edition of one of the most trusted books on timeseries analysis. Since publication of the first edition in 1970,Time Series Analysis has served as one of the most influential andprominent works on the subject. This new edition maintains itsbalanced presentation of the tools for modeling and analyzing timeseries and also introduces the latest developments that haveoccurred n the field over the past decade through applications fromareas such as business, finance, and engineering.

The Fourth Edition provides a clearly written exploration of thekey methods for building, classifying, testing, and analyzingstochastic models for time series as well as their use in fiveimportant areas of application: forecasting; determining thetransfer function of a system; modeling the effects of interventionevents; developing multivariate dynamic models; and designingsimple control schemes. Along with these classical uses, moderntopics are introduced through the book′s new features, whichinclude:

A new chapter on multivariate time series analysis, includinga discussion of the challenge that arise with their modeling and anoutline of the necessary analytical tools

New coverage of forecasting in the design of feedback andfeedforward control schemes

A new chapter on nonlinear and long memory models, whichexplores additional models for application such as heteroscedastictime series, nonlinear time series models, and models for longmemory 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 modelswith missing values

Numerous illustrations and detailed appendices supplement thebook,while extensive references and discussion questions at the endof each chapter facilitate an in–depth understanding of bothtime–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. thisbook is also an invaluable reference for applied statisticians,engineers, and financial analysts.

Reviews

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

Mathematical Reviews, 2009)

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

"I think the book is very valuable and useful to graduatestudents in statistics, mathematics, engineering, and thelike.  Also, it could be of tremendous help topractioners.  Even though the book is written in a clear, easyto follow narrative style with plenty of illustrations, one shouldnevertheless have a sufficient knowledge of graduate levelmathematical statistics.  By reading and understanding thebook one should, in the end, feel very confident in time series andanalysis." (MAA Reviews, January 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)

Back cover copy

A modernized new edition of one of the most trusted books on timeseries analysis. Since publication of the first edition in 1970,Time Series Analysis has served as one of the most influential andprominent works on the subject. This new edition maintains itsbalanced presentation of the tools for modeling and analyzing timeseries and also introduces the latest developments that haveoccurred n the field over the past decade through applications fromareas such as business, finance, and engineering.

The Fourth Edition provides a clearly written exploration of thekey methods for building, classifying, testing, and analyzingstochastic models for time series as well as their use in fiveimportant areas of application: forecasting; determining thetransfer function of a system; modeling the effects of interventionevents; developing multivariate dynamic models; and designingsimple control schemes. Along with these classical uses, moderntopics are introduced through the book′s new features, whichinclude:

A new chapter on multivariate time series analysis, includinga discussion of the challenge that arise with their modeling and anoutline of the necessary analytical tools

New coverage of forecasting in the design of feedback andfeedforward control schemes

A new chapter on nonlinear and long memory models, whichexplores additional models for application such as heteroscedastictime series, nonlinear time series models, and models for longmemory 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 modelswith missing values

Numerous illustrations and detailed appendices supplement thebook,while extensive references and discussion questions at the endof each chapter facilitate an in–depth understanding of bothtime–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. thisbook is also an invaluable reference for applied statisticians,engineers, and financial analysts.