PREFACE xi

1 INTRODUCTION TO FORECASTING 1
1.1 The Nature and Uses of Forecasts 1
1.2 Some Examples of Time Series 6
1.3 The Forecasting Process 13
1.4 Data for Forecasting 16
1.5 Resources for Forecasting 19

2 STATISTICS BACKGROUND FOR FORECASTING 25
2.1 Introduction 25
2.2 Graphical Displays 26
2.3 Numerical Description of Time Series Data 33
2.4 Use of Data Transformations and Adjustments 46
2.5 General Approach to Time Series Modeling and Forecasting 61
2.6 Evaluating and Monitoring Forecasting Model Performance 64
2.7 R Commands for Chapter 2 84

3 REGRESSION ANALYSIS AND FORECASTING 107
3.1 Introduction 107
3.2 Least Squares Estimation in Linear Regression Models 110
3.3 Statistical Inference in Linear Regression 119
3.4 Prediction of New Observations 134
3.5 Model Adequacy Checking 136
3.6 Variable Selection Methods in Regression 146
3.7 Generalized and Weighted Least Squares 152
3.8 Regression Models for General Time Series Data 177
3.9 Econometric Models 205
3.10 R Commands for Chapter 3 209

4 EXPONENTIAL SMOOTHING METHODS 233
4.1 Introduction 233
4.2 First-Order Exponential Smoothing 239
4.3 Modeling Time Series Data 245
4.4 Second-Order Exponential Smoothing 247
4.5 Higher-Order Exponential Smoothing 257
4.6 Forecasting 259
4.7 Exponential Smoothing for Seasonal Data 277
4.8 Exponential Smoothing of Biosurveillance Data 286
4.9 Exponential Smoothers and Arima Models 299
4.10 R Commands for Chapter 4 300

5 AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) MODELS 327
5.1 Introduction 327
5.2 Linear Models for Stationary Time Series 328
5.2.1 Stationarity 329
5.2.2 Stationary Time Series 329
5.3 Finite Order Moving Average Processes 333
5.4 Finite Order Autoregressive Processes 337
5.5 Mixed Autoregressive-Moving Average Processes 354
5.6 Nonstationary Processes 363
5.7 Time Series Model Building 367
5.8 Forecasting Arima Processes 378
5.9 Seasonal Processes 383
5.10 Arima Modeling of Biosurveillance Data 393
5.11 Final Comments 399
5.12 R Commands for Chapter 5 401

6 TRANSFER FUNCTIONS AND INTERVENTION MODELS 427
6.1 Introduction 427
6.2 Transfer Function Models 428
6.3 Transfer Function-Noise Models 436
6.4 Cross-Correlation Function 436
6.5 Model Specification 438
6.6 Forecasting with Transfer Function-Noise Models 456
6.7 Intervention Analysis 462
6.8 R Commands for Chapter 6 473

7 SURVEY OF OTHER FORECASTING METHODS 493
7.1 Multivariate Time Series Models and Forecasting 493
7.3 Arch and Garch Models 507
7.4 Direct Forecasting of Percentiles 512
7.5 Combining Forecasts to Improve Prediction Performance 518
7.6 Aggregation and Disaggregation of Forecasts 522
7.7 Neural Networks and Forecasting 526
7.8 Spectral Analysis 529
7.9 Bayesian Methods in Forecasting 535
7.10 Some Comments on Practical Implementation and Use of Statistical Forecasting Procedures 542
7.11 R Commands for Chapter 7 545

APPENDIX A STATISTICAL TABLES 561

APPENDIX B DATA SETS FOR EXERCISES 581

APPENDIX C INTRODUCTION TO R 627

BIBLIOGRAPHY 631

INDEX 639