Time Series Analysis : Forecasting and Control
by Box, George E. P.; Jenkins, Gwilym M.; Reinsel, Gregory C.Edition: 4th
Format: Hardcover
Pub. Date: 2008-06-30
Publisher(s): Wiley
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Summary
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.
Author Biography
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.
Table of Contents
| Preface to the Fourth Edition | p. xxi |
| Preface to the Third Edition | p. xxiii |
| Introduction | p. 1 |
| Five Important Practical Problems | |
| Stochastic and Deterministic Dynamic Mathematical Models | p. 7 |
| Basic Ideas in Model Building | p. 16 |
| Stochastic Models and Their Forecasting | p. 19 |
| Autocorrelation Function and Spectrum of Stationary Processes | p. 21 |
| Autocorrelation Properties of Stationary Models | p. 21 |
| Spectral Properties of Stationary Models | p. 35 |
| Link between the Sample Spectrum and Autocovariance Function Estimate | p. 45 |
| Linear Stationary Models | p. 47 |
| General Linear Process | p. 47 |
| Autoregressive Processes | p. 55 |
| Moving Average Processes | p. 71 |
| Mixed Autoregressive-Moving Average Processes | p. 79 |
| Autocovariances, Autocovariance Generating Function, and Stationarity Conditions for a General Linear Process | p. 86 |
| Recursive Method for Calculating Estimates of Autoregressive Parameters | p. 89 |
| Linear Nonstationary Models | p. 93 |
| Autoregressive Integrated Moving Average Processes | p. 93 |
| Three Explicit Forms for The Autoregressive Integrated Moving Average Model | p. 103 |
| Integrated Moving Average Processes | p. 114 |
| Linear Difference Equations | p. 125 |
| IMA(0, 1, 1) Process with Deterministic Drift | p. 131 |
| Arima Processes with Added Noise | p. 131 |
| Forecasting | p. 137 |
| Minimum Mean Square Error Forecasts and Their Properties | p. 137 |
| Calculating and Updating Forecasts | p. 145 |
| Forecast Function and Forecast Weights | p. 152 |
| Examples of Forecast Functions and Their Updating | p. 157 |
| Use of State-Space Model Formulation for Exact Forecasting | p. 170 |
| Summary | p. 177 |
| Correlations Between Forecast Errors | p. 180 |
| Forecast Weights for Any Lead Time | p. 182 |
| Forecasting in Terms of the General Integrated Form | p. 185 |
| Stochastic Model Building | p. 193 |
| Model Identification | p. 195 |
| Objectives of Identification | p. 195 |
| Identification Techniques | p. 196 |
| Initial Estimates for the Parameters | p. 213 |
| Model Multiplicity | p. 221 |
| Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process | p. 225 |
| General Method for Obtaining Initial Estimates of the Parameters of a Mixed Autoregressive-Moving Average Process | p. 226 |
| Model Estimation | p. 231 |
| Study of the Likelihood and Sum-of-Squares Functions | p. 231 |
| Nonlinear Estimation | p. 255 |
| Some Estimation Results for Specific Models | p. 268 |
| Likelihood Function Based on the State-Space Model | p. 275 |
| Unit Roots in Arima Models | p. 280 |
| Estimation Using Bayes's Theorem | p. 287 |
| Review of Normal Distribution Theory | p. 296 |
| Review of Linear Least Squares Theory | p. 303 |
| Exact Likelihood Function for Moving Average and Mixed Processes | p. 306 |
| Exact Likelihood Function for an Autoregressive Process | p. 314 |
| Asymptotic Distribution of Estimators for Autoregressive Models | p. 323 |
| Examples of the Effect of Parameter Estimation Errors on Variances of Forecast Errors and Probability Limits for Forecasts | p. 327 |
| Special Note on Estimation of Moving Average Parameters | p. 330 |
| Model Diagnostic Checking | p. 333 |
| Checking the Stochastic Model | p. 333 |
| Diagnostic Checks Applied to Residuals | p. 335 |
| Use of Residuals to Modify the Model | p. 350 |
| Seasonal Models | p. 353 |
| Parsimonious Models for Seasonal Time Series | p. 353 |
| Representation of the Airline Data by a Multiplicative (0, 1, 1) x (0, 1, 1)[subscript 12] Model | p. 359 |
| Some Aspects of More General Seasonal ARIMA Models | p. 375 |
| Structural Component Models and Deterministic Seasonal Components | p. 384 |
| Regression Models with Time Series Error Terms | p. 397 |
| Autocovariances for Some Seasonal Models | p. 407 |
| Nonlinear and Long Memory Models | p. 413 |
| Autoregressive Conditional Heteroscedastic (ARCH) Models | p. 413 |
| Nonlinear Time Series Models | p. 420 |
| Long Memory Time Series Processes | p. 428 |
| Transfer Function and Multivariate Model Building | p. 437 |
| Transfer Function Models | p. 439 |
| Linear Transfer Function Models | p. 439 |
| Discrete Dynamic Models Represented by Difference Equations | p. 447 |
| Relation Between Discrete and Continuous Models | p. 458 |
| Continuous Models with Pulsed Inputs | p. 465 |
| Nonlinear Transfer Functions and Linearization | p. 470 |
| Identification, Fitting, and Checking of Transfer Function Models | p. 473 |
| Cross-Correlation Function | p. 474 |
| Identification of Transfer Function Models | p. 481 |
| Fitting and Checking Transfer Function Models | p. 492 |
| Some Examples of Fitting and Checking Transfer Function Models | p. 501 |
| Forecasting With Transfer Function Models Using Leading Indicators | p. 509 |
| Some Aspects of the Design of Experiments to Estimate Transfer Functions | p. 519 |
| Use of Cross Spectral Analysis for Transfer Function Model Identification | p. 521 |
| Choice of Input to Provide Optimal Parameter Estimates | p. 524 |
| Intervention Analysis Models and Outlier Detection | p. 529 |
| Intervention Analysis Methods | p. 529 |
| Outlier Analysis for Time Series | p. 536 |
| Estimation for ARMA Models with Missing Values | p. 543 |
| Multivariate Time Series Analysis | p. 551 |
| Stationary Multivariate Time Series | p. 552 |
| Linear Model Representations for Stationary Multivariate Processes | p. 556 |
| Nonstationary Vector Autoregressive-Moving Average Models | p. 570 |
| Forecasting for Vector Autoregressive-Moving Average Processes | p. 573 |
| State-Space Form of the Vector ARMA Model | p. 575 |
| Statistical Analysis of Vector ARMA Models | p. 578 |
| Example of Vector ARMA Modeling | p. 588 |
| Design of Discrete Control Schemes | p. 597 |
| Aspects of Process Control | p. 599 |
| Process Monitoring and Process Adjustment | p. 600 |
| Process Adjustment Using Feedback Control | p. 604 |
| Excessive Adjustment Sometimes Required by MMSE Control | p. 620 |
| Minimum Cost Control with Fixed Costs of Adjustment and Monitoring | p. 623 |
| Feedforward Control | p. 627 |
| Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes | p. 642 |
| Feedback Control Schemes Where the Adjustment Variance is Restricted | p. 644 |
| Choice of the Sampling Interval | p. 653 |
| Charts and Tables | p. 659 |
| Collection of Tables and Charts | p. 661 |
| Collection of Time Series Used for Examples in the Text and in Exercises | p. 669 |
| References | p. 685 |
| Exercises and Problems | p. 701 |
| Index | p. 729 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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