Economic forecasting involves choosing simple yet robust models to best approximate highly complex and evolving data-generating processes. This poses unique challenges for researchers in a host of practical forecasting situations, from forecasting budget deficits and assessing financial risk to predicting inflation and stock market returns. Economic Forecasting presents a comprehensive, unified approach to assessing the costs and benefits of different methods currently available to forecasters.
This text approaches forecasting problems from the perspective of decision theory and estimation, and demonstrates the profound implications of this approach for how we understand variable selection, estimation, and combination methods for forecasting models, and how we evaluate the resulting forecasts. Both Bayesian and non-Bayesian methods are covered in depth, as are a range of cutting-edge techniques for producing point, interval, and density forecasts. The book features detailed presentations and empirical examples of a range of forecasting methods and shows how to generate forecasts in the presence of large-dimensional sets of predictor variables. The authors pay special attention to how estimation error, model uncertainty, and model instability affect forecasting performance.
• Presents a comprehensive and integrated approach to assessing the strengths and weaknesses of different forecasting methods
• Approaches forecasting from a decision theoretic and estimation perspective
• Covers Bayesian modeling, including methods for generating density forecasts
• Discusses model selection methods as well as forecast combinations
• Covers a large range of nonlinear prediction models, including regime switching models, threshold autoregressions, and models with time-varying volatility
• Features numerous empirical examples
• Examines the latest advances in forecast evaluation
• Essential for practitioners and students alike
Author(s): Graham Elliott, Allan Timmermann
Publisher: Princeton University Press
Year: 2016
Language: English
Pages: 567
City: Princeton and Oxford
Preface xiii
I Foundations
1 Introduction 3
1.1 Outline of the Book 3
1.2 Technical Notes 12
2 Loss Functions 13
2.1 Construction and Specification of the Loss Function 14
2.2 Specific Loss Functions 20
2.3 Multivariate Loss Functions 28
2.4 Scoring Rules for Distribution Forecasts 29
2.5 Examples of Applications of Forecasts in Macroeconomics and Finance 31
2.6 Conclusion 37
3 The Parametric Forecasting Problem 39
3.1 Optimal Point Forecasts 41
3.2 Classical Approach 47
3.3 Bayesian Approach 54
3.4 Relating the Bayesian and Classical Methods 56
3.5 Empirical Example: Asset Allocation with Parameter Uncertainty 59
3.6 Conclusion 62
4 Classical Estimation of Forecasting Models 63
4.1 Loss-Based Estimators 64
4.2 Plug-In Estimators 68
4.3 Parametric versus Nonparametric Estimation Approaches 73
4.4 Conclusion 74
5 Bayesian Forecasting Methods 76
5.1 Bayes Risk 77
5.2 Ridge and Shrinkage Estimators 81
5.3 Computational Methods 83
5.4 Economic Applications of Bayesian Forecasting Methods 85
5.5 Conclusion 88
6 Model Selection 89
6.1 Trade-Offs in Model Selection 90
6.2 Sequential Hypothesis Testing 93
6.3 Information Criteria 96
6.4 Cross Validation 99
6.5 Lasso Model Selection 101
6.6 Hard versus Soft Thresholds: Bagging 104
6.7 Empirical Illustration: Forecasting Stock Returns 106
6.8 Properties of Model Selection Procedures 115
6.9 Risk for Model Selection Methods: Monte Carlo Simulations 121
6.10 Conclusion 125
6.11 Appendix: Derivation of Information Criteria 126
II Forecast Methods
7 Univariate Linear Prediction Models 133
7.1 ARMA Models as Approximations 134
7.2 Estimation and Lag Selection for ARMA Models 142
7.3 Forecasting with ARMA Models 147
7.4 Deterministic and Seasonal Components 155
7.5 Exponential Smoothing and Unobserved Components 159
7.6 Conclusion 164
8 Univariate Nonlinear Prediction Models 166
8.1 Threshold Autoregressive Models 167
8.2 Smooth Transition Autoregressive Models 169
8.3 Regime Switching Models 172
8.4 Testing for Nonlinearity 179
8.5 Forecasting with Nonlinear Univariate Models 180
8.6 Conclusion 185
9 Vector Autoregressions 186
9.1 Specification of Vector Autoregressions 186
9.2 Classical Estimation of VARs 189
9.3 Bayesian VARs 194
9.4 DSGE Models 206
9.5 Conditional Forecasts 210
9.6 Empirical Example 212
9.7 Conclusion 217
10 Forecasting in a Data-Rich Environment 218
10.1 Forecasting with Factor Models 220
10.2 Estimation of Factors 223
10.3 Determining the Number of Common Factors 229
10.4 Practical Issues Arising with Factor Models 232
10.5 Empirical Evidence 234
10.6 Forecasting with Panel Data 241
10.7 Conclusion 243
11 Nonparametric Forecasting Methods 244
11.1 Kernel Estimation of Forecasting Models 245
11.2 Estimation of Sieve Models 246
11.3 Boosted Regression Trees 256
11.4 Conclusion 259
12 Binary Forecasts 260
12.1 Point and Probability Forecasts for Binary Outcomes 261
12.2 Density Forecasts for Binary Outcomes 265
12.3 Constructing Point Forecasts for Binary Outcomes 269
12.4 Empirical Application: Forecasting the Direction of
the Stock Market 272
12.5 Conclusion 273
13 Volatility and Density Forecasting 275
13.1 Role of the Loss Function 277
13.2 Volatility Models 278
13.3 Forecasts Using Realized Volatility Measures 288
13.4 Approaches to Density Forecasting 291
13.5 Interval and Quantile Forecasts 301
13.6 Multivariate Volatility Models 304
13.7 Copulas 306
13.8 Conclusion 308
14 Forecast Combinations 310
14.1 Optimal Forecast Combinations: Theory 312
14.2 Estimation of Forecast Combination Weights 316
14.3 Risk for Forecast Combinations 325
14.4 Model Combination 329
14.5 Density Combination 336
14.6 Bayesian Model Averaging 339
14.7 Empirical Evidence 341
14.8 Conclusion 344
III Forecast Evaluation
15 Desirable Properties of Forecasts 347
15.1 Informal Evaluation Methods 348
15.2 Loss Decomposition Methods 352
15.3 Efficiency Properties with Known Loss 355
15.4 Optimality Tests under Unknown Loss 365
15.5 Optimality Tests That Do Not Rely on Measuring the Outcome 368
15.6 Interpreting Efficiency Tests 368
15.7 Conclusion 371
16 Evaluation of Individual Forecasts 372
16.1 The Sampling Distribution of Average Losses 373
16.2 Simulating Out-of-Sample Forecasts 375
16.3 Conducting Inference on the Out-of-Sample Average Loss 380
16.4 Out-of-Sample Asymptotics for Rationality Tests 385
16.5 Evaluation of Aggregate versus Disaggregate Forecasts 388
16.6 Conclusion 390
17 Evaluation and Comparison of Multiple Forecasts 391
17.1 Forecast Encompassing Tests 393
17.2 Tests of Equivalent Expected Loss: The Diebold–Mariano Test 397
17.3 Comparing Forecasting Methods: The Giacomini–White Approach 400
17.4 Comparing Forecasting Performance across Nested Models 403
17.5 Comparing Many Forecasts 409
17.6 Addressing Data Mining 413
17.7 Identifying Superior Models 415
17.8 Choice of Sample Split 417
17.9 Relating the Methods 418
17.10 In-Sample versus Out-of-Sample Forecast Comparison 418
17.11 Conclusion 420
18 Evaluating Density Forecasts 422
18.1 Evaluation Based on Loss Functions 423
18.2 Evaluating Features of Distributional Forecasts 428
18.3 Tests Based on the Probability Integral Transform 433
18.4 Evaluation of Multicategory Forecasts 438
18.5 Evaluating Interval Forecasts 440
18.6 Conclusion 441
IV Refinements and Extensions
19 Forecasting under Model Instability 445
19.1 Breaks and Forecasting Performance 446
19.2 Limitations of In-Sample Tests for Model Instability 448
19.3 Models with a Single Break 451
19.4 Models with Multiple Breaks 455
19.5 Forecasts That Model the Break Process 456
19.6 Ad Hoc Methods for Dealing with Breaks 460
19.7 Model Instability and Forecast Evaluation 463
19.8 Conclusion 465
20
Trending Variables and Forecasting
467
20.1 Expected Loss with Trending Variables 468
20.2 Univariate Forecasting Models 470
20.3 Multivariate Forecasting Models 478
20.4 Forecasting with Persistent Regressors 480
20.5 Forecast Evaluation 486
20.6 Conclusion 489
21 Forecasting Nonstandard Data 490
21.1 Forecasting Count Data 491
21.2 Forecasting Durations 493
21.3 Real-Time Data 495
21.4 Irregularly Observed and Unobserved Data 498
21.5 Conclusion 504
Appendix 505
A.1 Kalman Filter 505
A.2 Kalman Filter Equations 507
A.3 Orders of Probability 514
A.4 Brownian Motion and Functional Central Limit Theory 515
Bibliography 517
Index 539
