Introduction to Time Series Analysis and

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 modelsBasic statistical tools used in analyzing time series dataMetrics for evaluating forecast errors and methods for evaluating and tracking forecasting performance over timeCross-section and time series regression data, least squares and maximum likelihood model fitting, model adequacy checking, prediction intervals, and weighted and generalized least squaresExponential smoothing techniques for time series with polynomial components and seasonal dataForecasting and prediction interval construction with a discussion on transfer function models as well as intervention modeling and analysisMultivariate time series problems, ARCH and GARCH models, and combinations of forecastsThe ARIMA model approach with a discussion on how to identify and fit these models for non-seasonal and seasonal time seriesThe intricate role of computer software in successful time series analysis is acknowledged with the use of Minitabr, JMPr, and SASr 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 PowerPointr 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.

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.

Preface	p. ix
Introduction to Forecasting	p. 1
The Nature and Uses of Forecasts	p. 1
Some Examples of Time Series	p. 5
The Forecasting Process	p. 12
Resources for Forecasting	p. 14
Exercises	p. 15
Statistics Background for Forecasting	p. 18
Introduction	p. 18
Graphical Displays	p. 19
Time Series Plots	p. 19
Plotting Smoothed Data	p. 22
Numerical Description of Time Series Data	p. 25
Stationary Time Series	p. 25
Autocovariance and Autocorrelation Functions	p. 28
Use of Data Transformations and Adjustments	p. 34
Transformations	p. 34
Trend and Seasonal Adjustments	p. 36
General Approach to Time Series Modeling and Forecasting	p. 46
Evaluating and Monitoring Forecasting Model Performance	p. 49
Forecasting Model Evaluation	p. 49
Choosing Between Competing Models	p. 57
Monitoring a Forecasting Model	p. 60
Exercises	p. 66
Regression Analysis and Forecasting	p. 73
Introduction	p. 73
Least Squares Estimation in Linear Regression Models	p. 75
Statistical Inference in Linear Regression	p. 84
Test for Significance of Regression	p. 84
Tests on Individual Regression Coefficients and Groups of Coefficients	p. 87
Confidence Intervals on Individual Regression Coefficients	p. 93
Confidence Intervals on the Mean Response	p. 94
Prediction of New Observations	p. 96
Model Adequacy Checking	p. 98
Residual Plots	p. 98
Scaled Residuals and PRESS	p. 100
Measures of Leverage and Influence	p. 105
Variable Selection Methods in Regression	p. 106
Generalized and Weighted Least Squares	p. 111
Generalized Least Squares	p. 112
Weighted Least Squares	p. 114
Discounted Least Squares	p. 119
Regression Models for General Time Series Data	p. 133
Detecting Autocorrelation: The Durbin-Watson Test	p. 134
Estimating the Parameters in Time Series Regression Models	p. 139
Exercises	p. 161
Exponential Smoothing Methods	p. 171
Introduction	p. 171
First-Order Exponential Smoothing	p. 176
The Initial Value, y[subscript 0]	p. 177
The Value of [lambda]	p. 178
Modeling Time Series Data	p. 180
Second-Order Exponential Smoothing	p. 183
Higher-Order Exponential Smoothing	p. 193
Forecasting	p. 193
Constant Process	p. 193
Linear Trend Process	p. 198
Estimation of [sigma subscript e superscript 2]	p. 207
Adaptive Updating of the Discount Factor	p. 208
Model Assessment	p. 209
Exponential Smoothing for Seasonal Data	p. 210
Additive Seasonal Model	p. 210
Multiplicative Seasonal Model	p. 214
Exponential Smoothers and ARIMA Models	p. 217
Exercises	p. 220
Autoregressive Integrated Moving Average (ARIMA) Models	p. 231
Introduction	p. 231
Linear Models for Stationary Time Series	p. 231
Stationarity	p. 232
Stationary Time Series	p. 233
Finite Order Moving Average (MA) Processes	p. 235
The First-Order Moving Average Process, MA(1)	p. 236
The Second-Order Moving Average Process, MA(2)	p. 238
Finite Order Autoregressive Processes	p. 239
First-Order Autoregressive Process, AR(1)	p. 240
Second-Order Autoregressive Process, AR(2)	p. 242
General Autoregressive Process, AR(p)	p. 246
Partial Autocorrelation Function, PACF	p. 248
Mixed Autoregressive-Moving Average (ARMA) Processes	p. 253
Nonstationary Processes	p. 256
Time Series Model Building	p. 265
Model Identification	p. 265
Parameter Estimation	p. 266
Diagnostic Checking	p. 266
Examples of Building ARIMA Models	p. 267
Forecasting ARIMA Processes	p. 275
Seasonal Processes	p. 282
Final Comments	p. 286
Exercises	p. 287
Transfer Functions and Intervention Models	p. 299
Introduction	p. 299
Transfer Function Models	p. 300
Transfer Function-Noise Models	p. 307
Cross Correlation Function	p. 307
Model Specification	p. 309
Forecasting with Transfer Function-Noise Models	p. 322
Intervention Analysis	p. 330
Exercises	p. 338
Survey of Other Forecasting Methods	p. 343
Multivariate Time Series Models and Forecasting	p. 343
Multivariate Stationary Process	p. 343
Vector ARIMA Models	p. 344
Vector AR (VAR) Models	p. 346
State Space Models	p. 350
ARCH and GARCH Models	p. 355
Direct Forecasting of Percentiles	p. 359
Combining Forecasts to Improve Prediction Performance	p. 365
Aggregation and Disaggregation of Forecasts	p. 369
Neural Networks and Forecasting	p. 372
Some Comments on Practical Implementation and Use of Statistical Forecasting Procedures	p. 375
Exercises	p. 378
Statistical Tables	p. 387
Data Sets for Exercises	p. 407
Bibliography	p. 437
Index	p. 443
Table of Contents provided by Ingram. All Rights Reserved.

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Introduction to Time Series Analysis and Forecasting

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