Introduction to Time Series Analysis and Forecasting

Douglas C. Montgomery, PhD, is Regents Professor of Industrial Engineering and ASU Foundation Professor of Engineering at Arizona State University, USA. He holds a PhD in Engineering from Virginia Tech and has researched and published extensively on industrial statistics and experimental design. Cheryl Jennings, PhD, is Associate Teaching Professor at Arizona State University. She has decades of industrial experience in manufacturing and financial services, and has taught undergraduate and graduate courses on modeling and analysis, performance management, process control, and related subjects. Murat Kulahci, PhD, is Professor of Industrial Statistics at the Technical University of Denmark and Professor at the Luleå University of Technology, Sweden. He holds a PhD in Industrial Engineering from the University of Wisconsin, Madison. He has published widely on time series analysis, experimental design, process monitoring and related subjects.

• Preface xiAbout the Companion Website xv1 Introduction to Time Series Analysis and Forecasting 11.1 The Nature and Uses of Forecasts 11.2 Some Examples of Time Series 91.3 The Forecasting Process 161.4 Data for Forecasting 191.4.1 The Data Warehouse 191.4.2 Data Wrangling and Cleaning 211.4.3 Imputation 221.5 Resources for Forecasting 23Exercises 242 Statistics Background for Time Series Analysis and Forecasting 272.1 Introduction 272.2 Graphical Displays 282.2.1 Time Series Plots 282.2.2 Plotting Smoothed Data 322.3 Numerical Description of Time Series Data 372.3.1 Stationary Time Series 372.3.2 Autocovariance and Autocorrelation Functions 392.3.3 The Variogram 452.4 Use of Data Transformations and Adjustments 492.4.1 Transformations 492.4.2 Trend and Seasonal Adjustments 512.5 General Approach to Time Series Modeling and Forecasting 652.6 Evaluating and Monitoring Forecasting Model Performance 692.6.1 Forecasting Model Evaluation 692.6.2 Choosing Between Competing Models 782.6.3 Monitoring a Forecasting Model 812.7 R Commands for Chapter 2 89Exercises 1013 Regression Analysis and Forecasting 1153.1 Introduction 1153.2 Least Squares Estimation in Linear Regression Models 1183.3 Statistical Inference in Linear Regression 1273.3.1 Test for Significance of Regression 1283.3.2 Tests on Individual Regression Coefficients and Groups of Coefficients 1313.3.3 Confidence Intervals on Individual Regression Coefficients 1373.3.4 Confidence Intervals on the Mean Response 1383.4 Prediction of New Observations 1413.5 Model Adequacy Checking 1433.5.1 Residual Plots 1433.5.2 Scaled Residuals and PRESS 1463.5.3 Measures of Leverage and Influence 1513.6 Variable Selection Methods in Regression 1533.7 Generalized and Weighted Least Squares 1603.7.1 Generalized Least Squares 1603.7.2 Weighted Least Squares 1633.7.3 Discounted Least Squares 1683.8 Regression Models for General Time Series Data 1843.8.1 Detecting Autocorrelation: The Durbin–Watson Test 1863.8.2 Estimating the Parameters in Time Series Regression Models 1913.9 Econometric Models 2133.10 R Commands for Chapter 3 216Exercises 2264 Exponential Smoothing Methods 2434.1 Introduction 2434.2 First-Order Exponential Smoothing 2494.2.1 The Initial Value, ỹ0 2514.2.2 The Value of λ 2514.3 Modeling Time Series Data 2544.4 Second-Order Exponential Smoothing 2574.5 Higher-Order Exponential Smoothing 2694.6 Forecasting 2704.6.1 Constant Process 2704.6.2 Linear Trend Process 2724.6.3 Estimation of σe2 2844.6.4 Adaptive Updating of the Discount Factor 2854.6.5 Model Assessment 2874.7 Exponential Smoothing for Seasonal Data 2884.7.1 Additive Seasonal Model 2884.7.2 Multiplicative Seasonal Model 2924.8 Exponential Smoothing of Biosurveillance Data 2994.9 Exponential Smoothers and ARIMA Models 3084.10 R Commands for Chapter 4 309Exercises 3215 Autoregressive Integrated Moving Average (ARIMA) Models 3395.1 Introduction 3395.2 Linear Models for Stationary Time Series 3405.2.1 Stationarity 3415.2.2 Stationary Time Series 3415.3 Finite Order Moving Average Processes 3455.3.1 The First-Order Moving Average Process, MA(1) 3475.3.2 The Second-Order Moving Average Process, MA(2) 3495.4 Finite Order Autoregressive Processes 3505.4.1 First-Order Autoregressive Process, AR(1) 3505.4.2 Second-Order Autoregressive Process, AR(2) 3545.4.3 General Autoregressive Process, AR(p) 3595.4.4 Partial Autocorrelation Function, PACF 3605.5 Mixed Autoregressive–Moving Average Processes 3675.5.1 Stationarity of ARMA(p, q) Process 3685.5.2 Invertibility of ARMA(p, q) Process 3685.5.3 ACF and PACF of ARMA(p, q) Process 3695.6 Nonstationary Processes 3765.6.1 Some Examples of ARIMA(p, d, q) Processes 3775.7 Time Series Model Building 3805.7.1 Model Identification 3805.7.2 Parameter Estimation 3815.7.3 Diagnostic Checking 3825.7.4 Examples of Building ARIMA Models 3835.8 Forecasting Arima Processes 3925.9 Seasonal Processes 4015.10 Arima Modeling of Biosurveillance Data 4075.11 Final Comments 4135.12 R Commands for Chapter 5 415Exercises 4276 Transfer Functions and Intervention Models 4476.1 Introduction 4476.2 Transfer Function Models 4486.3 Transfer Function–Noise Models 4566.4 Cross-Correlation Function 4566.5 Model Specification 4586.6 Forecasting with Transfer Function–Noise Models 4766.7 Intervention Analysis 4816.8 R Commands for Chapter 6 494Exercises 5087 Other Time Series Analysis and Forecasting Methods 5177.1 Multivariate Time Series Models and Forecasting 5177.1.1 Multivariate Stationary Process 5187.1.2 Vector ARIMA Models 5197.1.3 Vector AR (VAR) Models 5207.2 State Space Models 5267.3 Arch and Garch Models 5317.4 Direct Forecasting of Percentiles 5367.5 Combining Forecasts to Improve Prediction Performance 5427.6 Aggregation and Disaggregation of Forecasts 5477.7 Neural Networks and Forecasting 5517.8 Spectral Analysis 5597.9 Bayesian Methods in Forecasting 5657.10 Some Comments on Practical Implementation and Use of Statistical Forecasting Procedures 5727.11 R Commands for Chapter 7 576Exercises 581Appendix A Statistical Tables 595Appendix B Data Sets for Exercises 615Appendix C Introduction to R 683Bibliography 689Index 697