PDF高清晰文字版

Contents

Preface xv
Chapter 1 Introduction and Overview
1.1. Purpose 1
1.2. Time Series 2
1.3. Missing Data 3
1.4. Sample Size 3
1.5. Representativeness 4
1.6. Scope of Application 4
1.7. Stochastic and Deterministic Processes 5
1.8. Stationarity 5
1.9. Methodological Approaches 7
1.10. Importance 9
1.11. Notation 9
1.11.1. Gender 9
1.11.2. Summation 10
1.11.3. Expectation 11
1.11.4. Lag Operator 12
1.11.5. The Difference Operator 12
1.11.6. Mean-Centering the Series 12
References 13

Chapter 2 Extrapolative and Decomposition Models
2.1. Introduction 15
2.2. Goodness-of-Fit Indicators 15
2.3. Averaging Techniques 18
2.3.1. The Simple Average 18
2.3.2. The Single Moving Average 18
2.3.3. Centered Moving Averages 20
2.3.4. Double Moving Averages 20
2.3.5. Weighted Moving Averages 22
2.4. Exponential Smoothing 23
2.4.1. Simple Exponential Smoothing 23
2.4.2. Holt’s Linear Exponential Smoothing 32
2.4.3. The Dampened Trend Linear Exponential Smoothing Model 38
2.4.4. Exponential Smoothing for Series with Trend and Seasonality: Winter’s Methods 39
2.4.5. Basic Evaluation of Exponential Smoothing 43
2.5. Decomposition Methods 45
2.5.1. Components of a Series 45
2.5.2. Trends 46
2.5.3. Seasonality 50
2.5.4. Cycles 50
2.5.5. Background 50
2.5.6. Overview of X-11 52
2.6. New Features of Census X-12 66
References 66

Chapter 3 Introduction to Box–Jenkins Time Series Analysis
3.1. Introduction 69
3.2. The Importance of Time Series Analysis Modeling 69
3.3. Limitations 70
3.4. Assumptions 70
3.5. Time Series 74
3.5.1. Moving Average Processes 74
3.5.2. Autoregressive Processes 76
3.5.3. ARMA Processes 77
3.5.4. Nonstationary Series and Transformations
to Stationarity 77
3.6. Tests for Nonstationarity 81
3.6.1. The Dickey–Fuller Test 81
3.6.2. Augmented Dickey–Fuller Test 84
3.6.3. Assumptions of the Dickey–Fuller and
Augmented Dickey–Fuller Tests 85
3.6.4. Programming the Dickey–Fuller Test 86
3.7. Stabilizing the Variance 90
3.8. Structural or Regime Stability 92
3.9. Strict Stationarity 93
3.10. Implications of Stationarity 94
3.10.1. For Autoregression 94
3.10.2. Implications of Stationarity for Moving
Average Processes 97
References 99

Chapter 4 The Basic ARIMA Model
4.1. Introduction to ARIMA 101
4.2. Graphical Analysis of Time Series Data 102
4.2.1. Time Sequence Graphs 102
4.2.2. Correlograms and Stationarity 106
4.3. Basic Formulation of the Autoregressive
Integrated Moving Average Model 108
4.4. The Sample Autocorrelation Function 110
4.5. The Standard Error of the ACF 118
4.6. The Bounds of Stationarity and Invertibility 119
4.7. The Sample Partial Autocorrelation Function 122
4.7.1. Standard Error of the PACF 125
4.8. Bounds of Stationarity and Invertibility Reviewed 125
4.9. Other Sample Autocorrelation Functions 126
4.10. Tentative Identification of Characteristic Patterns of
Integrated, Autoregressive, Moving Average, and ARMA Processes 128
4.10.1. Preliminary Programming Syntax for Identification of the Model 128
4.10.2. Stationarity Assessment 132
4.10.3. Identifying Autoregressive Models 134
4.10.4. Identifying Moving Average Models 137
4.10.5. Identifying Mixed Autoregressive–Moving Average Models 142
References 149

Chapter 5 Seasonal ARIMA Models
5.1. Cyclicity 151
5.2. Seasonal Nonstationarity 154
5.3. Seasonal Differencing 161
5.4. Multiplicative Seasonal Models 162
5.4.1. Seasonal Autoregressive Models 164
5.4.2. Seasonal Moving Average Models 166
5.4.3. Seasonal Autoregressive Moving Average Models 168
5.5. The Autocorrelation Structure of Seasonal ARIMA Models 169
5.6. Stationarity and Invertibility of Seasonal ARIMA Models 170
5.7. A Modeling Strategy for the Seasonal ARIMA Model 171
5.7.1. Identification of Seasonal Nonstationarity 171
5.7.2. Purely Seasonal Models 171
5.7.3. A Modeling Strategy for General Multiplicative Seasonal Models 173
5.8. Programming Seasonal Multiplicative Box–Jenkins Models 183
5.8.1. SAS Programming Syntax 183
5.8.2. SPSS Programming Syntax 185
5.9. Alternative Methods of Modeling Seasonality 186
5.10. The Question of Deterministic or Stochastic Seasonality 188
References 189

Chapter 6 Estimation and Diagnosis
6.1. Introduction 191
6.2. Estimation 191
6.2.1. Conditional Least Squares 192
6.2.2. Unconditional Least Squares 195
6.2.3. Maximum Likelihood Estimation 198
6.2.4. Computer Applications 204
6.3. Diagnosis of the Model 208
References 213

Chapter 7 Metadiagnosis and Forecasting
7.1. Introduction 215
7.2. Metadiagnosis 217
7.2.1. Statistical Program Output of Metadiagnostic Criteria 221
7.3. Forecasting with Box–Jenkins Models 222
7.3.1. Forecasting Objectives 222
7.3.2. Basic Methodology of Forecasting 224
7.3.3. The Forecast Function 225
7.3.4. The Forecast Error 232
7.3.5. Forecast Error Variance 232
7.3.6. Forecast Confidence Intervals 233
7.3.7. Forecast Profiles for Basic Processes 234
7.4. Characteristics of the Optimal Forecast 244
7.5. Basic Combination of Forecasts 245
7.6. Forecast Evaluation 248
7.7. Statistical Package Forecast Syntax 251
7.7.1. Introduction 251
7.7.2. SAS Syntax 252
7.7.3. SPSS Syntax 254
7.8. Regression Combination of Forecasts 256
References 263

Chapter 8 Intervention Analysis
8.1. Introduction: Event Interventions and Their Impacts 265
8.2. Assumptions of the Event Intervention (Impact) Model 267
8.3. Impact Analysis Theory 268
8.3.1. Intervention Indicators 268
8.3.2. The Intervention (Impulse Response) Function 270
8.3.3. The Simple Step Function: Abrupt Onset,Permanent Duration 270
8.3.4. First-Order Step Function: Gradual Onset,Permanent Duration 272
8.3.5. Abrupt Onset, Temporary Duration 276
8.3.6. Abrupt Onset and Oscillatory Decay 278
8.3.7. Graduated Onset and Gradual Decay 279
8.4. Significance Tests for Impulse Response Functions 280
8.5. Modeling Strategies for Impact Analysis 282
8.5.1. The Box–Jenkins–Tiao Strategy 283
8.5.2. Full Series Modeling Strategy 285
8.6. Programming Impact Analysis 288
8.6.1. An Example of SPSS Impact Analysis Syntax 290
8.6.2. An Example of SAS Impact Analysis Syntax 297
8.6.3. Example: The Impact of Watergate on Nixon Presidential Approval Ratings 314
8.7. Applications of Impact Analysis 342
8.8. Advantages of Intervention Analysis 345
8.9. Limitations of Intervention Analysis 346
References 350

Chapter 9 Transfer Function Models
9.1. Definition of a Transfer Function 353
9.2. Importance 354
9.3. Theory of the Transfer Function Model 355
9.3.1. The Assumption of the Single-Input Case 355
9.3.2. The Basic Nature of the Single-Input Transfer Function 355
9.4. Modeling Strategies 368
9.4.1. The Conventional Box–Jenkins Modeling Strategy 368
9.4.2. The Linear Transfer Function Modeling Strategy 399
9.5. Cointegration 420
9.6. Long-Run and Short-Run Effects in Dynamic Regression 421
9.7. Basic Characteristics of a Good Time Series Model 422
References 423

Chapter 10 Autoregressive Error Models
10.1. The Nature of Serial Correlation of Error 425
10.1.1. Regression Analysis and the Consequences of Autocorrelated Error 426
10.2. Sources of Autoregressive Error 435
10.3. Autoregressive Models with Serially Correlated Errors 437
10.4. Tests for Serial Correlation of Error 437
10.5. Corrective Algorithms for Regression Models with Autocorrelated Error 439
10.6. Forecasting with Autocorrelated Error Models 441
10.7. Programming Regression with Autocorrelated Errors 443
10.7.1. SAS PROC AUTOREG 443
10.7.2. SPSS ARIMA Procedures for Autoregressive Error Models 452
10.8. Autoregression in Combining Forecasts 458
10.9. Models with Stochastic Variance 462
10.9.1. ARCH and GARCH Models 463
10.9.2. ARCH Models for Combining Forecasts 464
References 465

Chapter 11 A Review of Model and Forecast Evaluation
11.1. Model and Forecast Evaluation 467
11.2. Model Evaluation 468
11.3. Comparative Forecast Evaluation 469
11.3.1. Capability of Forecast Methods 471
11.4. Comparison of Individual Forecast Methods 476
11.5. Comparison of Combined Forecast Models 477
References 478

Chapter 12 Power Analysis and Sample Size Determination for Well-Known Time Series Models Monnie McGee
12.1. Census X-11 482
12.2. Box–Jenkins Models 483
12.3. Tests for Nonstationarity 486
12.4. Intervention Analysis and Transfer Functions 487
12.5. Regression with Autoregressive Errors 490
12.6. Conclusion 491
References 492
Appendix A 495
Glossary 497
Index 513