Handbook of Economic Forecasting part 2 pps

Introduction to the Series vPART 1: FORECASTING METHODOLOGY Chapter 1 Bayesian Forecasting 2.2.. Distribution-forecast and distribution-realization loss functions 97 Chapter 3 Forecast E

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Introduction to the Series v

PART 1: FORECASTING METHODOLOGY

Chapter 1

Bayesian Forecasting

2.2 Model completion with prior distributions 10

2.3 Model combination and evaluation 14

3.1 Simulation methods before 1990 25

4.1 In the beginning, there was diffuseness, conjugacy, and analytic work 41

4.4 After Minnesota: Subsequent developments 49

5.1 Autoregressive leading indicator models 54

5.4 Cointegration and error correction 61

6.1 National BVAR forecasts: The Federal Reserve Bank of Minneapolis 69

6.2 Regional BVAR forecasts: Economic conditions in Iowa 70

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xii Contents of Volume 1

Chapter 2

Forecasting and Decision Theory

1.3 Forecasting versus statistical hypothesis testing and estimation 87

2.3 Recovery of decision problems from loss functions 93

2.4 Location-dependent loss functions 96

2.5 Distribution-forecast and distribution-realization loss functions 97

Chapter 3

Forecast Evaluation

Chapter 4

Forecast Combinations

2.1 Specification of loss function 141

2.2 Construction of a super model – pooling information 143

2.3 Linear forecast combinations under MSE loss 144

2.4 Optimality of equal weights – general case 148

2.5 Optimal combinations under asymmetric loss 150

2.6 Combining as a hedge against non-stationarities 154

3.1 To combine or not to combine 156

3.2 Least squares estimators of the weights 158

3.3 Relative performance weights 159

3.5 Nonparametric combination schemes 160

3.6 Pooling, clustering and trimming 162

4.2 Nonlinear combination schemes 169

5.1 Shrinkage and factor structure 172

5.2 Constraints on combination weights 174

6 Combination of interval and probability distribution forecasts 176

6.2 Combinations of probability density forecasts 177

6.4 Combinations of quantile forecasts 179

7.1 Simple combination schemes are hard to beat 181

7.2 Choosing the single forecast with the best track record is often a bad idea 182

7.3 Trimming of the worst models often improves performance 183

7.4 Shrinkage often improves performance 184

7.5 Limited time-variation in the combination weights may be helpful 185

Chapter 5

Predictive Density Evaluation

Part II: Testing for Correct Specification of Conditional Distributions 207

xiv Contents of Volume 1

2.1 Diebold, Gunther and Tay approach – probability integral transform 208

2.2 Bai approach – martingalization 208

2.3 Hong and Li approach – a nonparametric test 210

2.4 Corradi and Swanson approach 212

2.5 Bootstrap critical values for the V 1T and V 2Ttests 216

3.1 Estimation and parameter estimation error in recursive and rolling estimation schemes – West as well as West and McCracken results 221

3.2 Out-of-sample implementation of Bai as well as Hong and Li tests 223

3.3 Out-of-sample implementation of Corradi and Swanson tests 225

3.4 Bootstrap critical for the V 1P ,J and V 2P ,J tests under recursive estimation 228

3.5 Bootstrap critical for the V 1P ,J and V 2P ,J tests under rolling estimation 233 Part III: Evaluation of (Multiple) Misspecified Predictive Models 234

4 Pointwise comparison of (multiple) misspecified predictive models 234

4.1 Comparison of two nonnested models: Diebold and Mariano test 235

4.2 Comparison of two nested models 238

4.3 Comparison of multiple models: The reality check 242

4.4 A predictive accuracy test that is consistent against generic alternatives 249

5 Comparison of (multiple) misspecified predictive density models 253

5.1 The Kullback–Leibler information criterion approach 253

5.2 A predictive density accuracy test for comparing multiple misspecified models 254

PART 2: FORECASTING MODELS

Chapter 6

Forecasting with VARMA Models

1.2 Notation, terminology, abbreviations 291

2.2 Cointegrated I (1) processes 294

2.3 Linear transformations of VARMA processes 294

2.4 Forecasting 296

3.2 Estimation of VARMA models for given lag orders and cointegrating rank 311

3.3 Testing for the cointegrating rank 313

3.4 Specifying the lag orders and Kronecker indices 314

Chapter 7

Forecasting with Unobserved Components Time Series Models

2.5 Surveys and measurement error 343

3.1 ARIMA models and the reduced form 348

3.3 Model selection in ARIMA, autoregressive and structural time series models 350

xvi Contents of Volume 1

6.5 Maximum likelihood estimation and the prediction error decomposition 368

6.6 Missing observations, temporal aggregation and mixed frequency 369

7.1 Seemingly unrelated times series equation models 370

7.2 Reduced form and multivariate ARIMA models 371

7.5 Forecasting and nowcasting with auxiliary series 379

9.2 Conditionally Gaussian models 394

9.3 Count data and qualitative observations 394

9.4 Heavy-tailed distributions and robustness 399

10.1 Basic specification and properties 404

Chapter 8

Forecasting Economic Variables with Nonlinear Models

1 Introduction 416

2.2 Nonlinear dynamic regression model 417

2.3 Smooth transition regression model 418

2.4 Switching regression and threshold autoregressive model 420

2.6 Artificial neural network model 422

2.7 Time-varying regression model 423

2.8 Nonlinear moving average models 424

3.3 Building switching regression models 429

3.4 Building Markov-switching regression models 431

4.2 Numerical techniques in forecasting 433

4.3 Forecasting using recursion formulas 436

4.4 Accounting for estimation uncertainty 437

4.5 Interval and density forecasts 438

4.7 Different models for different forecast horizons? 439

7.2 Comparing linear and nonlinear models 447

Chapter 9

Approximate Nonlinear Forecasting Methods

xviii Contents of Volume 1

4.2 Generically comprehensively revealing activation functions 475

5.1 A prototype QuickNet algorithm 477

6.1 Interpreting approximation-based forecasts 485

6.2 Explaining remarkable forecast outcomes 485

6.3 Explaining adverse forecast outcomes 490

7.1 Estimating nonlinear forecasting models 492

7.2 Explaining forecast outcomes 505

PART 3: FORECASTING WITH PARTICULAR DATA STRUCTURES

Chapter 10

Forecasting with Many Predictors

1.1 Many predictors: Opportunities and challenges 517

2 The forecasting environment and pitfalls of standard forecasting methods 518

2.2 Pitfalls of using standard forecasting methods when n is large 519

3.1 Forecast combining setup and notation 521

3.2 Large-n forecast combining methods 522

3.3 Survey of the empirical literature 523

4.2 DFM estimation by maximum likelihood 527

4.3 DFM estimation by principal components analysis 528

4.4 DFM estimation by dynamic principal components analysis 532

4.5 DFM estimation by Bayes methods 533

4.6 Survey of the empirical literature 533

5 Bayesian model averaging 535

5.1 Fundamentals of Bayesian model averaging 536

5.2 Survey of the empirical literature 541

6.1 Empirical Bayes methods for large-n linear forecasting 543

7.2 Data and comparison methodology 547

Chapter 11

Forecasting with Trending Data

7.1 Evaluating and comparing expected losses 596

7.2 Orthogonality and unbiasedness regressions 598

7.3 Cointegration of forecasts and outcomes 599

Chapter 12

Forecasting with Breaks

2.1 General (model-free) forecast-error taxonomy 609

2.2 VAR model forecast-error taxonomy 613

3.1 Conditional variance processes 614