Student Solutions Manual to Accompany Introduction to Time Series Analysis and Forecasting

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

2. Statistics Background for Forecasting 18

2.1 Introduction, 18

2.2 Graphical Displays, 19

2.3 Numerical Description of Time Series Data, 25

2.4 Use of Data Transformations and Adjustments, 34

2.5 General Approach to Time Series Modeling and Forecasting, 46

2.6 Evaluating and Monitoring Forecasting Model Performance, 49

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

3.4 Prediction of New Observations, 96

3.5 Model Adequacy Checking, 98

3.6 Variable Selection Methods in Regression, 106

3.7 Generalized and Weighted Least Squares, 111

3.8 Regression Models for General Time Series Data, 133

4. Exponential Smoothing Methods 171

4.1 Introduction, 171

4.2 First-Order Exponential Smoothing, 176

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

4.7 Exponential Smoothing for Seasonal Data, 210

4.8 Exponential Smoothers and ARIMA Models, 217

5. Autoregressive Integrated Moving Average (ARIMA) Models 231

5.1 Introduction, 231

5.2 Linear Models for Stationary Time Series, 231

5.3 Finite Order Moving Average (MA) Processes, 235

5.4 Finite Order Autoregressive Processes, 239

5.5 Mixed Autoregressive–Moving Average (ARMA) Processes, 253

5.6 Nonstationary Processes, 256

5.7 Time Series Model Building, 265

5.8 Forecasting ARIMA Processes, 275

5.9 Seasonal Processes, 282

5.10 Final Comments, 286

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

7. Survey of Other Forecasting Methods 343

7.1 Multivariate Time Series Models and Forecasting, 343

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

Appendix A. Statistical Tables 387

Appendix B. Data Sets for Exercises 407

Bibliography 437

Index 443