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CONTENTS OF VOLUME 1
Introduction to the Series v
Contents of the Handbook vii
PART 1: FORECASTING METHODOLOGY
Chapter 1
Bayesian Forecasting
JOHN GEWEKE AND CHARLES WHITEMAN 3
Abstract 4
Keywords 4
1. Introduction 6
2. Bayesian inference and forecasting: A primer 7
2.1. Models for observables 7
2.2. Model completion with prior distributions 10
2.3. Model combination and evaluation 14
2.4. Forecasting 19
3. Posterior simulation methods 25
3.1. Simulation methods before 1990 25
3.2. Markov chain Monte Carlo 30
3.3. The full Monte 36
4. ’Twas not always so easy: A historical perspective 41
4.1. In the beginning, there was diffuseness, conjugacy, and analytic work 41
4.2. The dynamic linear model 43
4.3. The Minnesota revolution 44
4.4. After Minnesota: Subsequent developments 49
5. Some Bayesian forecasting models 53
5.1. Autoregressive leading indicator models 54
5.2. Stationary linear models 56
5.3. Fractional integration 59
5.4. Cointegration and error correction 61
5.5. Stochastic volatility 64

3. A small number of nonnested models, Part I 104
4. A small number of nonnested models, Part II 106
5. A small number of nonnested models, Part III 111
6. A small number of models, nested: MPSE 117
7. A small number of models, nested, Part II 122
8. Summary on small number of models 125
9. Large number of models 125
10. Conclusions 131
Acknowledgements 132
References 132
Chapter 4
Forecast Combinations
ALLAN TIMMERMANN 135
Abstract 136
Keywords 136
1. Introduction 137
2. The forecast combination problem 140
Contents of Volume 1 xiii
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. Estimation 156
3.1. To combine or not to combine 156
3.2. Least squares estimators of the weights 158
3.3. Relative performance weights 159
3.4. Moment estimators 160

Part II: Testing for Correct Specification of Conditional Distributions 207
xiv Contents of Volume 1
2. Specification testing and model evaluation in-sample 207
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
2T
tests 216
2.6. Other related work 220
3. Specification testing and model selection out-of-sample 220
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

3. Specifying and estimating VARMA models 306
3.1. The echelon form 306
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
3.5. Diagnostic checking 316
4. Forecasting with estimated processes 316
4.1. General results 316
4.2. Aggregated processes 318
5. Conclusions 319
Acknowledgements 321
References 321
Chapter 7
Forecasting with Unobserved Components Time Series Models
ANDREW HARVEY 327
Abstract 330
Keywords 330
1. Introduction 331
1.1. Historical background 331
1.2. Forecasting performance 333
1.3. State space and beyond 334
2. Structural time series models 335
2.1. Exponential smoothing 336
2.2. Local level model 337
2.3. Trends 339
2.4. Nowcasting 340
2.5. Surveys and measurement error 343
2.6. Cycles 343
2.7. Forecasting components 344
2.8. Convergence models 347

7.5. Forecasting and nowcasting with auxiliary series 379
8. Continuous time 383
8.1. Transition equations 383
8.2. Stock variables 385
8.3. Flow variables 387
9. Nonlinear and non-Gaussian models 391
9.1. General state space model 392
9.2. Conditionally Gaussian models 394
9.3. Count data and qualitative observations 394
9.4. Heavy-tailed distributions and robustness 399
9.5. Switching regimes 401
10. Stochastic volatility 403
10.1. Basic specification and properties 404
10.2. Estimation 405
10.3. Comparison with GARCH 405
10.4. Multivariate models 406
11. Conclusions 406
Acknowledgements 407
References 408
Chapter 8
Forecasting Economic Variables with Nonlinear Models
TIMO TERÄSVIRTA 413
Abstract 414
Keywords 415
Contents of Volume 1 xvii
1. Introduction 416
2. Nonlinear models 416
2.1. General 416
2.2. Nonlinear dynamic regression model 417
2.3. Smooth transition regression model 418

HALBERT WHITE 459
Abstract 460
Keywords 460
1. Introduction 461
2. Linearity and nonlinearity 463
2.1. Linearity 463
2.2. Nonlinearity 466
xviii Contents of Volume 1
3. Linear, nonlinear, and highly nonlinear approximation 467
4. Artificial neural networks 474
4.1. General considerations 474
4.2. Generically comprehensively revealing activation functions 475
5. QuickNet 476
5.1. A prototype QuickNet algorithm 477
5.2. Constructing 
m
479
5.3. Controlling overfit 480
6. Interpretational issues 484
6.1. Interpreting approximation-based forecasts 485
6.2. Explaining remarkable forecast outcomes 485
6.3. Explaining adverse forecast outcomes 490
7. Empirical examples 492
7.1. Estimating nonlinear forecasting models 492
7.2. Explaining forecast outcomes 505
8. Summary and concluding remarks 509
Acknowledgements 510
References 510
PART 3: FORECASTING WITH PARTICULAR DATA STRUCTURES
Chapter 10

7.3. Empirical results 547
8. Discussion 549
References 550
Chapter 11
Forecasting with Trending Data
GRAHAM ELLIOTT 555
Abstract 556
Keywords 556
1. Introduction 557
2. Model specification and estimation 559
3. Univariate models 563
3.1. Short horizons 565
3.2. Long run forecasts 575
4. Cointegration and short run forecasts 581
5. Near cointegrating models 586
6. Predicting noisy variables with trending regressors 591
7. Forecast evaluation with unit or near unit roots 596
7.1. Evaluating and comparing expected losses 596
7.2. Orthogonality and unbiasedness regressions 598
7.3. Cointegration of forecasts and outcomes 599
8. Conclusion 600
References 601
Chapter 12
Forecasting with Breaks
MICHAEL P. CLEMENTS AND DAVID F. HENDRY 605
Abstract 606
Keywords 606
1. Introduction 607
2. Forecast-error taxonomies 609
2.1. General (model-free) forecast-error taxonomy 609