Economic Forecasting

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 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 A comprehensive and integrated approach to economic forecasting problemsEconomic 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 methodsApproaches forecasting from a decision theoretic and estimation perspectiveCovers Bayesian modeling, including methods for generating density forecastsDiscusses model selection methods as well as forecast combinationsCovers a large range of nonlinear prediction models, including regime switching models, threshold autoregressions, and models with time-varying volatilityFeatures numerous empirical examplesExamines the latest advances in forecast evaluationEssential for practitioners and students alike A comprehensive and integrated approach to economic forecasting problems 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. "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." --Descripción del editor 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.-- Provided by Publisher