Introduction to Time Series Analysis and Forecasting: (Wiley Series in Probability and Statistics)

An accessible introduction to the most current thinking in and practicality of forecasting techniques in the context of time-oriented data. Analyzing time-oriented data and forecasting are among the most important problems that analysts face across many fields, ranging from finance and economics to production operations and the natural sciences. As a result, there is a widespread need for large groups of people in a variety of fields to understand the basic concepts of time series analysis and forecasting. Introduction to Time Series Analysis and Forecasting presents the time series analysis branch of applied statistics as the underlying methodology for developing practical forecasts, and it also bridges the gap between theory and practice by equipping readers with the tools needed to analyze time-oriented data and construct useful, short- to medium-term, statistically based forecasts. Seven easy-to-follow chapters provide intuitive explanations and in-depth coverage of key forecasting topics, including: Regression-based methods, heuristic smoothing methods, and general time series models Basic statistical tools used in analyzing time series data Metrics for evaluating forecast errors and methods for evaluating and tracking forecasting performance over time Cross-section and time series regression data, least squares and maximum likelihood model fitting, model adequacy checking, prediction intervals, and weighted and generalized least squares Exponential smoothing techniques for time series with polynomial components and seasonal data Forecasting and prediction interval construction with a discussion on transfer function models as well as intervention modeling and analysis Multivariate time series problems, ARCH and GARCH models, and combinations of forecasts The ARIMA model approach with a discussion on how to identify and fit these models for non-seasonal and seasonal time series The intricate role of computer software in successful time series analysis is acknowledged with the use of Minitab, JMP, and SAS software applications, which illustrate how the methods are imple-mented in practice. An extensive FTP site is available for readers to obtain data sets, Microsoft Office PowerPoint slides, and selected answers to problems in the book. Requiring only a basic working knowledge of statistics and complete with exercises at the end of each chapter as well as examples from a wide array of fields, Introduction to Time Series Analysis and Forecasting is an ideal text for forecasting and time series courses at the advanced undergraduate and beginning graduate levels. The book also serves as an indispensable reference for practitioners in business, economics, engineering, statistics, mathematics, and the social, environmental, and life sciences.

Table of Contents:
Preface ix 1. Introduction to Forecasting 1 1.1 The Nature and Uses of Forecasts 1 1.2 Some Examples of Time Series 5 1.3 The Forecasting Process 12 1.4 Resources for Forecasting 14 Exercises 15 2. Statistics Background for Forecasting 18 2.1 Introduction 18 2.2 Graphical Displays 19 2.2.1 Time Series Plots 19 2.2.2 Plotting Smoothed Data 22 2.3 Numerical Description of Time Series Data 25 2.3.1 Stationary Time Series 25 2.3.2 Autocovariance and Autocorrelation Functions 28 2.4 Use of Data Transformations and Adjustments 34 2.4.1 Transformations 34 2.4.2 Trend and Seasonal Adjustments 36 2.5 General Approach to Time Series Modeling and Forecasting 46 2.6 Evaluating and Monitoring Forecasting Model Performance 49 2.6.1 Forecasting Model Evaluation 49 2.6.2 Choosing Between Competing Models 57 2.6.3 Monitoring a Forecasting Model 60 Exercises 66 3. Regression Analysis and Forecasting 73 3.1 Introduction 73 3.2 Least Squares Estimation in Linear Regression Models 75 3.3 Statistical Inference in Linear Regression 84 3.3.1 Test for Significance of Regression 84 3.3.2 Tests on Individual Regression Coefficients and Groups of Coefficients 87 3.3.3 Confidence Intervals on Individual Regression Coefficients 93 3.3.4 Confidence Intervals on the Mean Response 94 3.4 Prediction of New Observations 96 3.5 Model Adequacy Checking 98 3.5.1 Residual Plots 98 3.5.2 Scaled Residuals and PRESS 100 3.5.3 Measures of Leverage and Influence 105 3.6 Variable Selection Methods in Regression 106 3.7 Generalized and Weighted Least Squares 111 3.7.1 Generalized Least Squares 112 3.7.2 Weighted Least Squares 114 3.7.3 Discounted Least Squares 119 3.8 Regression Models for General Time Series Data 133 3.8.1 Detecting Autocorrelation: The Durbin–Watson Test 134 3.8.2 Estimating the Parameters in Time Series Regression Models 139 Exercises 161 4. Exponential Smoothing Methods 171 4.1 Introduction 171 4.2 First-Order Exponential Smoothing 176 4.2.1 The Initial Value y0 177 4.2.2 The Value of λ 178 4.3 Modeling Time Series Data 180 4.4 Second-Order Exponential Smoothing 183 4.5 Higher-Order Exponential Smoothing 193 4.6 Forecasting 193 4.6.1 Constant Process 193 4.6.2 Linear Trend Process 198 4.6.3 Estimation of σ2e 207 4.6.4 Adaptive Updating of the Discount Factor 208 4.6.5 Model Assessment 209 4.7 Exponential Smoothing for Seasonal Data 210 4.7.1 Additive Seasonal Model 210 4.7.2 Multiplicative Seasonal Model 214 4.8 Exponential Smoothers and ARIMA Models 217 Exercises 220 5. Autoregressive Integrated Moving Average (ARIMA) Models 231 5.1 Introduction 231 5.2 Linear Models for Stationary Time Series 231 5.2.1 Stationarity 232 5.2.2 Stationary Time Series 233 5.3 Finite Order Moving Average (MA) Processes 235 5.3.1 The First-Order Moving Average Process MA(1) 236 5.3.2 The Second-Order Moving Average Process MA(2) 238 5.4 Finite Order Autoregressive Processes 239 5.4.1 First-Order Autoregressive Process AR(1) 240 5.4.2 Second-Order Autoregressive Process AR(2) 242 5.4.3 General Autoregressive Process AR(p) 246 5.4.4 Partial Autocorrelation Function PACF 248 5.5 Mixed Autoregressive–Moving Average (ARMA) Processes 253 5.6 Nonstationary Processes 256 5.7 Time Series Model Building 265 5.7.1 Model Identification 265 5.7.2 Parameter Estimation 266 5.7.3 Diagnostic Checking 266 5.7.4 Examples of Building ARIMA Models 267 5.8 Forecasting ARIMA Processes 275 5.9 Seasonal Processes 282 5.10 Final Comments 286 Exercises 287 6. Transfer Functions and Intervention Models 299 6.1 Introduction 299 6.2 Transfer Function Models 300 6.3 Transfer Function–Noise Models 307 6.4 Cross Correlation Function 307 6.5 Model Specification 309 6.6 Forecasting with Transfer Function–Noise Models 322 6.7 Intervention Analysis 330 Exercises 338 7. Survey of Other Forecasting Methods 343 7.1 Multivariate Time Series Models and Forecasting 343 7.1.1 Multivariate Stationary Process 343 7.1.2 Vector ARIMA Models 344 7.1.3 Vector AR (VAR) Models 346 7.2 State Space Models 350 7.3 ARCH and GARCH Models 355 7.4 Direct Forecasting of Percentiles 359 7.5 Combining Forecasts to Improve Prediction Performance 365 7.6 Aggregation and Disaggregation of Forecasts 369 7.7 Neural Networks and Forecasting 372 7.8 Some Comments on Practical Implementation and Use of Statistical Forecasting Procedures 375 Exercises 378 Appendix A. Statistical Tables 387 Appendix B. Data Sets for Exercises 407 Bibliography 437 Index 443

About the Author :
Douglas C. Montgomery, PhD, is Regents' Professor of Industrial Engineering and Statistics at Arizona State University. Dr. Montgomery has over thirty years of academic and consulting experience and has devoted his research to engineering statistics, specifically the design and analysis of experiments, statistical methods for process monitoring and optimization, and the analysis of time-oriented data. He has authored or coauthored over 190 journal articles and eleven books, including Introduction to Linear Regression Analysis, Fourth Edition and Generalized Linear Models: With Applications in Engineering and the Sciences, both published by Wiley. Cheryl L. Jennings, PhD, is a Process Design Consultant with Bank of America. An active member of both the American Statistical Association and the American Society for Quality, her areas of research and professional interest include Six Sigma; modeling and analysis; and process control and improvement. Dr. Jennings earned her PhD in industrial engineering from Arizona State University. Murat Kulahci, PhD, is Associate Professor in Informatics and Mathematical Modelling at the Technical University of Denmark. He has authored or coauthored over thirty journal articles in the areas of time series analysis, design of experiments, and statistical process control and monitoring.

Review :
"This would be an appropriate source for use in a first course in time series analysis. It might also be useful as a reference for researchers who want to apply time series analysis to their data sets." (CHOICE, October 2008) "The result is a book that can be used with a wide variety of audiences, with different interests and technical backgrounds, whose common interests are understanding how to analyze time-oriented data and constructing good short-term statistically based forecasts." (Mathematical Reviews, 2008m) "The book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics." (MAA Reviews, July 2008)