Introduction to Time Series Analysis and Forecasting

DOUGLAS C. MONTGOMERY, PhD, is Regents' Professor and ASU Foundation Professor of Engineering at Arizona State University. With over 35 years of academic and consulting experience, Dr. Montgomery has authored or coauthored over 250 journal articles and 13 books. His research interests include design and analysis of experiments, statistical methods for process monitoring and optimization, and the analysis of time-oriented data. CHERYL L. JENNINGS, PhD, is Faculty Associate at Arizona State University. With more than 30 years of experience in the automotive, semiconductor, and banking industries, Dr. Jennings has coauthored two books. Her areas of professional interest include Six Sigma, modeling and analysis, performance management, and process control and improvement. MURAT KULAHCI, PhD, is Associate Professor of Statistics at the Technical University of Denmark and Guest Deputy Professor at the Luleå University of Technology in Sweden. He is the author and/or coauthor of over 60 journal articles and two books. Dr. Kulahci's research interests include time series analysis, design of experiments, and statistical process control and monitoring.

• preface xi1 Introduction to Forecasting 11.1 The Nature and Uses of Forecasts 11.2 Some Examples of Time Series 61.3 The Forecasting Process 131.4 Data for Forecasting 161.4.1 The Data Warehouse 161.4.2 Data Cleaning 181.4.3 Imputation 181.5 Resources for Forecasting 19Exercises 202 Statistics Background for Forecasting 252.1 Introduction 252.2 Graphical Displays 262.2.1 Time Series Plots 262.2.2 Plotting Smoothed Data 302.3 Numerical Description of Time Series Data 332.3.1 Stationary Time Series 332.3.2 Autocovariance and Autocorrelation Functions 362.3.3 The Variogram 422.4 Use of Data Transformations and Adjustments 462.4.1 Transformations 462.4.2 Trend and Seasonal Adjustments 482.5 General Approach to Time Series Modeling and Forecasting 612.6 Evaluating and Monitoring Forecasting Model Performance 642.6.1 Forecasting Model Evaluation 642.6.2 Choosing Between Competing Models 742.6.3 Monitoring a Forecasting Model 772.7 R Commands for Chapter 2 84Exercises 963 Regression Analysis and Forecasting 1073.1 Introduction 1073.2 Least Squares Estimation in Linear Regression Models 1103.3 Statistical Inference in Linear Regression 1193.3.1 Test for Significance of Regression 1203.3.2 Tests on Individual Regression Coefficients and Groups of Coefficients 1233.3.3 Confidence Intervals on Individual Regression Coefficients 1303.3.4 Confidence Intervals on the Mean Response 1313.4 Prediction of New Observations 1343.5 Model Adequacy Checking 1363.5.1 Residual Plots 1363.5.2 Scaled Residuals and PRESS 1393.5.3 Measures of Leverage and Influence 1443.6 Variable Selection Methods in Regression 1463.7 Generalized and Weighted Least Squares 1523.7.1 Generalized Least Squares 1533.7.2 Weighted Least Squares 1563.7.3 Discounted Least Squares 1613.8 Regression Models for General Time Series Data 1773.8.1 Detecting Autocorrelation: The Durbin–Watson Test 1783.8.2 Estimating the Parameters in Time Series Regression Models 1843.9 Econometric Models 2053.10 R Commands for Chapter 3 209Exercises 2194 Exponential Smoothing Methods 2334.1 Introduction 2334.2 First-Order Exponential Smoothing 2394.2.1 The Initial Value, ̃y0 2414.2.2 The Value of 𝜆 2414.3 Modeling Time Series Data 2454.4 Second-Order Exponential Smoothing 2474.5 Higher-Order Exponential Smoothing 2574.6 Forecasting 2594.6.1 Constant Process 2594.6.2 Linear Trend Process 2644.6.3 Estimation of 𝜎2e 2734.6.4 Adaptive Updating of the Discount Factor 2744.6.5 Model Assessment 2764.7 Exponential Smoothing for Seasonal Data 2774.7.1 Additive Seasonal Model 2774.7.2 Multiplicative Seasonal Model 2804.8 Exponential Smoothing of Biosurveillance Data 2864.9 Exponential Smoothers and Arima Models 2994.10 R Commands for Chapter 4 300Exercises 3115 Autoregressive Integrated Moving Average (Arima) Models 3275.1 Introduction 3275.2 Linear Models for Stationary Time Series 3285.2.1 Stationarity 3295.2.2 Stationary Time Series 3295.3 Finite Order Moving Average Processes 3335.3.1 The First-Order Moving Average Process, MA(1) 3345.3.2 The Second-Order Moving Average Process, MA(2) 3365.4 Finite Order Autoregressive Processes 3375.4.1 First-Order Autoregressive Process, AR(1) 3385.4.2 Second-Order Autoregressive Process, AR(2) 3415.4.3 General Autoregressive Process, AR(p) 3465.4.4 Partial Autocorrelation Function, PACF 3485.5 Mixed Autoregressive–Moving Average Processes 3545.5.1 Stationarity of ARMA(p, q) Process 3555.5.2 Invertibility of ARMA(p, q) Process 3555.5.3 ACF and PACF of ARMA(p, q) Process 3565.6 Nonstationary Processes 3635.6.1 Some Examples of ARIMA(p, d, q) Processes 3635.7 Time Series Model Building 3675.7.1 Model Identification 3675.7.2 Parameter Estimation 3685.7.3 Diagnostic Checking 3685.7.4 Examples of Building ARIMA Models 3695.8 Forecasting Arima Processes 3785.9 Seasonal Processes 3835.10 Arima Modeling of Biosurveillance Data 3935.11 Final Comments 3995.12 R Commands for Chapter 5 401Exercises 4126 Transfer Functions and Intervention Models 4276.1 Introduction 4276.2 Transfer Function Models 4286.3 Transfer Function–Noise Models 4366.4 Cross-Correlation Function 4366.5 Model Specification 4386.6 Forecasting with Transfer Function–Noise Models 4566.7 Intervention Analysis 4626.8 R Commands for Chapter 6 473Exercises 4867 Survey of Other Forecasting Methods 4937.1 Multivariate Time Series Models and Forecasting 4937.1.1 Multivariate Stationary Process 4947.1.2 Vector ARIMA Models 4947.1.3 Vector AR (VAR) Models 4967.2 State Space Models 5027.3 Arch and Garch Models 5077.4 Direct Forecasting of Percentiles 5127.5 Combining Forecasts to Improve Prediction Performance 5187.6 Aggregation and Disaggregation of Forecasts 5227.7 Neural Networks and Forecasting 5267.8 Spectral Analysis 5297.9 Bayesian Methods in Forecasting 5357.10 Some Comments on Practical Implementation and Use of Statistical Forecasting Procedures 5427.11 R Commands for Chapter 7 545Exercises 550Appendix A Statistical Tables 561Appendix B Data Sets for Exercises 581Appendix C Introduction to R 627Bibliography 631Index 639