Time Series Analysis

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.

Preface to the Fourth Edition. Preface to the Third Edition. 1. Introduction. 1.1 Five Important Practical Problems. 1.2 Stochastic and Deterministic Dynamic Mathematical Models. Part One: Stochastic Models and Their Forecasting. 2. Autocorrelation Function and Spectrum of Stationary Processes. 2.1 Autocorelation 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 Integrated Moving Average Model. 4.3 Integrated Moving Average Processes. 5. Forecasting. 5.1 Minimum Mean Square Error Forecasts and Their Properties. 5.2 Calculating and Updating Forecasts. 5.3 Forecast Function and Forecast Wrights. 5.4 Example of Forecast Functions and Their Updating. 5.5 Use of State-Space Model Formulation for Exact Forecasting. 5.6 Summary. Part Two: Stochastic Model Building. 6. Model Identification. 6.1 Objective of Identification. 6.2 Indetification 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. 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. 9.3 Some Aspects of More General Seasonal ARIMA Models. 9.4 Structural Component Models and Deterministic Seasonal Components. 9.5 Regression Models with Time Error Terms. 10. Nonlinear and Long Memory Models. 10.1 Autoregressive Conditional Heteroscedastic (ARCH) Models. 10.2 Nonlinear Time Series Models. 10.3 Long memory Time Series Processes. Part Three: Transfer Function and Multivariate Model Building. 11. Transfer Function Models. 11.1 Linear Transfer Function Models. 11.2 Discrete Dynamic Models Represented by Difference Equations. 11.3 Relation Between Discrete and Continuous Models. 12. Identification, Fitting, and Checking of Transfer Function Models. 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 Function Models. 12.5 Forecasting with Transfer Function Models Using Leading Indicators. 12.6 Some Aspects of the Design of Experiments to Estimate Transfer Functions. 13. Intervention Analysis Models and Outlier Detection. 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 Multivariate Processes. 14.3 Nonstationary Vector Autoregressive-Moving Average Models. 14.4 Forecasting for Vector Autoregressive-Moving Average Processes. 14.5 State-Space Form of the Vector ARMA Models. 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 Sometime Required by MMSE Control. 15.4 Minimum Cost Control with Fixed Costs of Adjustment and Monitoring. 15.5 Feedforward Control. 15.6 Monitoring Values of Parameters of Forecasting and Feedback Adjustment Schemes. Part Five: Charts and Tables. Collection of Tables and Charts. Collection of Time Series Used for Examples in the Text and in Exercises. References. Part Six: Exercises and Problems. Index.