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# Time series analysis: forecasting and control

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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

Available at all branches.

- There are no reservable copies for this title. Please contact a member of library staff for further information.

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.

- Preface to the Fourth Edition xxi
- Preface to the Third Edition xxiii
- 1 Introduction
- 1.1 Five Important Practical Problems
- 1.2 Stochastic and Deterministic Dynamic Mathematical Models,7
- 1.3 Basic Ideas in Model Building
- Part One Stochastic Models and Their Forecasting
- 2 Autocorrelation Function and Spectrum of StationaryProcesses
- 2.1 Autocorrelation Properties of Stationary Models
- 2.2 Spectral Properties of Stationary Models
- 3 Linear Stationary Models
- 3.1 General Linear Process
- 3.2 Autoregressive Processes
- 3.3 Moving Average Processes
- 3.4 Mixed Autoregressive Moving Average Processes
- 4 Linear Nonstationary Models
- 4.1 Autoregressive Integrated Moving Average Processes
- 4.2 Three Explicit Forms for The Autoregressive IntegratedMoving Average Model
- 4.3 Integrated Moving Average Processes
- 5 Forecasting
- 5.1 Minimum Mean Square Error Forecasts and Their Properties,137
- 5.2 Calculating and Updating Forecasts
- 5.3 Forecast Function and Forecast Weights
- 5.4 Examples of Forecast Functions and Their Updating
- 5.5 Use of State–Space Model Formulation for Exact Forecasting,170
- 5.6 Summary
- Part Two Stochastic Model Building
- 6 Model Identification
- 6.1 Objectives of Identification
- 6.2 Identification Techniques
- 6.3 Initial Estimates for the Parameters
- 6.4 Model Multiplicity
- 7 Model Estimation
- 7.1 Study of the Likelihood and Sum–of–Squares Functions,231
- 7.2 Nonlinear Estimation
- 7.3 Some Estimation Results for Specific Models
- 7.4 Likelihood Function Based on the State–Space Model
- 7.5 Unit Roots in Arima Models
- 7.6 Estimation Using Bayes s Theorem
- 8 Model Diagnostic Checking
- 8.1 Checking the Stochastic Model
- 8.2 Diagnostic Checks Applied to Residuals
- 8.3 Use of Residuals to Modify the Model
- 9 Seasonal Models
- 9.1 Parsimonious Models for Seasonal Time Series
- 9.2 Representation of the Airline Data by a Multiplicative (0,1, 1) × (0, 1, 1)12 Model
- 9.3 Some Aspects of More General Seasonal ARIMA Models
- 9.4 Structural Component Models and Deterministic SeasonalComponents
- 9.5 Regression Models with Time Series Error Terms
- 10 Nonlinear and Long Memory Models
- 10.1 Autoregressive Conditional Heteroscedastic (ARCH) Models,413
- 10.2 Nonlinear Time Series Models
- 10.3 Long Memory Time Series Processes
- Part Three Transfer Function and Multivariate Model Building437
- 11 Transfer Function Models
- 11.1 Linear Transfer Function Models
- 11.2 Discrete Dynamic Models Represented by DifferenceEquations
- 11.3 Relation Between Discrete and Continuous Models
- 12 Identification, Fitting, and Checking of Transfer FunctionModels
- 12.1 Cross–Correlation Function
- 12.2 Identification of Transfer Function Models
- 12.3 Fitting and Checking Transfer Function Models
- 12.4 Some Examples of Fitting and Checking Transfer FunctionModels
- 12.5 Forecasting With Transfer Function Models Using LeadingIndicators
- 12.6 Some Aspects of the Design of Experiments to EstimateTransfer Functions
- 13 Intervention Analysis Models and Outlier Detection529
- 13.1 Intervention Analysis Methods
- 13.2 Outlier Analysis for Time Series
- 13.3 Estimation for ARMA Models with Missing Values
- 14 Multivariate Time Series Analysis
- 14.1 Stationary Multivariate Time Series
- 14.2 Linear Model Representations for Stationary MultivariateProcesses
- 14.3 Nonstationary Vector Autoregressive Moving AverageModels
- 14.4 Forecasting for Vector Autoregressive Moving AverageProcesses
- 14.5 State–Space Form of the Vector ARMA Model
- 14.6 Statistical Analysis of Vector ARMA Models
- 14.7 Example of Vector ARMA Modeling
- Part Four Design of Discrete Control Schemes
- 15 Aspects of Process Control
- 15.1 Process Monitoring and Process Adjustment
- 15.2 Process Adjustment Using Feedback Control
- 15.3 Excessive Adjustment Sometimes Required by MMSE Control,620
- 15.4 Minimum Cost Control with Fixed Costs of Adjustment andMonitoring
- 15.5 Feedforward Control
- 15.6 Monitoring Values of Parameters of Forecasting and FeedbackAdjustment Schemes
- Part Five Charts and Tables
- Collection of Tables and Charts
- Collection of Time Series Used for Examples in the Text and inExercises
- References
- Part Six Exercises and Problems
- Index

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.

?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)

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.