Time Series Analysis - George E. P. Box

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Résumé :

Preface to the Fifth Edition xix

Preface to the Fourth Edition xxiii

Preface to the Third Edition xxv

1 Introduction 1

1.1 Five Important Practical Problems 2

1.2 Stochastic and Deterministic Dynamic Mathematical Models 6

1.3 Basic Ideas in Model Building 14

Appendix A. 1 Use of the R Software 17

Exercises 18

Part One Stochastic Models and Their Forecasting 19

2 Autocorrelation Function and Spectrum of Stationary Processes 21

2.1 Autocorrelation Properties of Stationary Models 21

2.2 Spectral Properties of Stationary Models 34

Appendix A2. 1 Link Between the Sample Spectrum and Autocovariance Function Estimate 43

Exercises 44

3 Linear Stationary Models 47

3.1 General Linear Process 47

3.2 Autoregressive Processes 54

3.3 Moving Average Processes 68

3.4 Mixed Autoregressive--Moving Average Processes 75

Appendix A3. 1 Autocovariances Autocovariance Generating Function, and Stationarity Conditions for a General Linear Process 82

Appendix A3. 2 Recursive Method for Calculating Estimates of Autoregressive Parameters 84

Exercises 86

4 Linear Nonstationary Models 88

4.1 Autoregressive Integrated Moving Average Processes 88

4.2 Three Explicit Forms for the ARIMA Model 97

4.3 Integrated Moving Average Processes 106

Appendix A4. 1 Linear Difference Equations 116

Appendix A4. 2 IMA(0, 1, 1) Process with Deterministic Drift 121

Appendix A4. 3 ARIMA Processes with Added Noise 122

Exercises 126

5 Forecasting 129

5.1 Minimum Mean Square Error Forecasts and Their Properties 129

5.2 Calculating Forecasts and Probability Limits 135

5.3 Forecast Function and Forecast Weights 139

5.4 Examples of Forecast Functions and Their Updating 144

5.5 Use of State-Space Model Formulation for Exact Forecasting 155

5.6 Summary 162

Appendix A5. 1 Correlation Between Forecast Errors 164

Appendix A5. 2 Forecast Weights for any Lead Time 166

Appendix A5. 3 Forecasting in Terms of the General Integrated Form 168

Exercises 174

Part Two STOCHASTIC MODEL BUILDING 177

6 Model Identification 179

6.1 Objectives of Identification 179

6.2 Identification Techniques 180

6.3 Initial Estimates for the Parameters 194

6.4 Model Multiplicity 202

Appendix A6. 1 Expected Behavior of the Estimated Autocorrelation Function for a Nonstationary Process 206

Exercises 207

7 Parameter Estimation 209

7.1 Study of the Likelihood and Sum-of-Squares Functions 209

7.2 Nonlinear Estimation 226

7.3 Some Estimation Results for Specific Models 236

7.4 Likelihood Function Based on the State-Space Model 242

7.5 Estimation Using Bayes' Theorem 245

Appendix A7. 1 Review of Normal Distribution Theory 251

Appendix A7. 2 Review of Linear Least-Squares Theory 256

Appendix A7. 3 Exact Likelihood Function for Moving Average and Mixed Processes 259

Appendix A7. 4 Exact Likelihood Function for an Autoregressive Process 266

Appendix A7. 5 Asymptotic Distribution of Estimators for Autoregressive Models 274

Appendix A7. 6 Examples of the Effect of Parameter Estimation Errors on Variances of Forecast Errors and Probability Limits for Forecasts 277

Appendix A. 7 Special Note on Estimation of Moving Average Parameters 280

Exercises 280

8 Model Diagnostic Checking 284

8.1 Checking the Stochastic Model 284

8.2 Diagnostic Checks Applied to Residuals 287

8.3 Use of Residuals to Modify the Mo...

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Praise for the Fourth Edition

The book follows faithfully the style of the original edition. The approach is heavily motivated by real-world time series, and by developing a complete approach to model building, estimation, forecasting and control.
-Mathematical Reviews

Bridging classical models and modern topics, the Fifth Edition of Time Series Analysis: Forecasting and Control maintains a balanced presentation of the tools for modeling and analyzing time series. Also describing? the latest developments that have occurred in the field over the past decade through applications from areas such as business, finance, and engineering, the Fifth Edition continues to serve as one of the most influential and prominent works on the subject.

Time Series Analysis: Forecasting and Control, Fifth Edition provides a clearly written exploration of the key methods for building, classifying, testing, and analyzing stochastic models for time series and describes their use in five important areas of application: forecasting...