Handbook Economic Forecasting Volume 1

Handbook Economic Forecasting Volume 1

(Parte 1 de 5)

HANDBOOK OF ECONOMIC FORECASTING VOLUME 1

Series Editors

VOLUME 1

Edited by

ALLAN TIMMERMANN University of California, San Diego

North-Holland is an imprint of Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK

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Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress

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ISBN-13: 978-0-4-51395-3 ISBN-10: 0-4-51395-7

ISSN: 0169-7218 (Handbooks in Economics series) ISSN: 1574-0706 (Handbook of Economic Forecasting series)

For information on all North-Holland publications visit our website at books.elsevier.com

The aim of the Handbooks in Economics series is to produce Handbooks for various branches of economics, each of which is a definitive source, reference, and teaching supplement for use by professional researchers and advanced graduate students. Each Handbook provides self-contained surveys of the current state of a branch of economics in the form of chapters prepared by leading specialists on various aspects of this branch of economics. These surveys summarize not only received results but also newer developments, from recent journal articles and discussion papers. Some original material is also included, but the main goal is to provide comprehensive and accessible surveys. The Handbooks are intended to provide not only useful reference volumes for professional collections but also possible supplementary readings for advanced courses for graduate students in economics.

KENNETH J. ARROW and MICHAEL D. INTRILIGATOR

For a complete overview of the Handbooks in Economics Series, please refer to the listing at the end of this volume.

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VOLUME1 Introduction to the Series Contents of the Handbook

PART1: FORECASTINGMETHODOLOGY

Chapter 1 Bayesian Forecasting John Geweke and Charles Whiteman

Chapter 2 Forecasting and Decision Theory Clive W.J. Granger and Mark J. Machina

Chapter 3 Forecast Evaluation Kenneth D. West

Chapter 4 Forecast Combinations Allan Timmermann

Chapter 5 Predictive Density Evaluation Valentina Corradi and Norman R. Swanson

PART 2: FORECASTING MODELS

Chapter 6 Forecasting with VARMA Models Helmut Lütkepohl

Chapter 7 Forecasting with Unobserved Components Time Series Models Andrew Harvey

Chapter 8 Forecasting Economic Variables with Nonlinear Models Timo Teräsvirta vii viii Contents of the Handbook

Chapter 9 Approximate Nonlinear Forecasting Methods Halbert White

PART3: FORECASTINGWITH PARTICULARDATASTRUCTURES

Chapter 10 Forecasting with Many Predictors James H. Stock and Mark W. Watson

Chapter 1 Forecasting with Trending Data Graham Elliott

Chapter 12 Forecasting with Breaks Michael P. Clements and David F. Hendry

Chapter 13 Forecasting Seasonal Time Series Eric Ghysels, Denise R. Osborn and Paulo M.M. Rodrigues

PART 4: APPLICATIONS OF FORECASTING METHODS

Chapter 14 Survey Expectations M. Hashem Pesaran and Martin Weale

Chapter 15 Volatility and Correlation Forecasting Torben G. Andersen, Tim Bollerslev, Peter F. Christoffersen and Francis X. Diebold

Chapter 16 Leading Indicators Massimiliano Marcellino

Chapter 17 Forecasting with Real-Time Macroeconomic Data Dean Croushore

Chapter 18 Forecasting in Marketing Philip Hans Franses

Contents of the Handbook ix

Author Index I-1 Subject Index I-19

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CONTENTSOFVOLUME1

Introduction to the Series v Contents of the Handbook vii

PART1: FORECASTINGMETHODOLOGY

Chapter 1 Bayesian Forecasting JOHNGEWEKEANDCHARLESWHITEMAN 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 4 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 6. Practical experience with Bayesian forecasts 68 6.1. National BVAR forecasts: The Federal Reserve Bank of Minneapolis 69 6.2. Regional BVAR forecasts: Economic conditions in Iowa 70 References 73 xii Contents of Volume 1

Chapter 2 Forecasting and Decision Theory CLIVE W.J. GRANGER ANDMARK J. MACHINA 81 Abstract 82 Keywords 82 Preface 83 1. History of the field 83 1.1. Introduction 83 1.2. The Cambridge papers 84 1.3. Forecasting versus statistical hypothesis testing and estimation 87 2. Forecasting with decision-based loss functions 87 2.1. Background 87 2.2. Framework and basic analysis 8 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 References 98

Chapter 3 Forecast Evaluation KENNETHD.WEST 9 Abstract 100 Keywords 100 1. Introduction 101 2. A brief history 102 3. A small number of nonnested models, Part I 104 4. A small number of nonnested models, Part I 106 5. A small number of nonnested models, Part I 1 6. A small number of models, nested: MPSE 117 7. A small number of models, nested, Part I 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 ALLANTIMMERMANN 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 3.5. Nonparametric combination schemes 160 3.6. Pooling, clustering and trimming 162 4. Time-varying and nonlinear combination methods 165 4.1. Time-varying weights 165 4.2. Nonlinear combination schemes 169 5. Shrinkage methods 170 5.1. Shrinkage and factor structure 172 5.2. Constraints on combination weights 174 6. Combination of interval and probability distribution forecasts 176 6.1. The combination decision 176 6.2. Combinations of probability density forecasts 177 6.3. Bayesian methods 178 6.4. Combinations of quantile forecasts 179 7. Empirical evidence 181 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 7.6. Empirical application 186 8. Conclusion 193 Acknowledgements 193 References 194

Chapter 5 Predictive Density Evaluation VALENTINACORRADIANDNORMANR.SWANSON 197 Abstract 198 Keywords 199 Part I: Introduction 200 1. Estimation, specification testing, and model evaluation 200 Part I: 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 V1T and V2T 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 V1P,J and V2P,J tests under recursive estimation 228

3.5. Bootstrap critical for the V1P,J and V2P,J tests under rolling estimation 233 Part I: 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

Acknowledgements 271 Part IV: Appendices and References 271 Appendix A: Assumptions 271 Appendix B: Proofs 275 References 280

PART2: FORECASTING MODELS

Chapter 6 Forecasting with VARMA Models HELMUTLÜTKEPOHL 287 Abstract 288 Keywords 288 1. Introduction and overview 289 1.1. Historical notes 290 1.2. Notation, terminology, abbreviations 291 2. VARMA processes 292 2.1. Stationary processes 292 2.2. Cointegrated I(1) processes 294 2.3. Linear transformations of VARMA processes 294

Contents of Volume 1 xv

2.4. Forecasting 296 2.5. Extensions 305 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 ANDREWHARVEY 327 Abstract 330 Keywords 330 1. Introduction 331 1.1. Historical background 331 1.2. Forecasting performance 3 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 3. ARIMA and autoregressive models 348 3.1. ARIMA models and the reduced form 348 3.2. Autoregressive models 350 3.3. Model selection in ARIMA, autoregressive and structural time series models 350 3.4. Correlated components 351 4. Explanatory variables and interventions 352 4.1. Interventions 354 4.2. Time-varying parameters 355 5. Seasonality 355 5.1. Trigonometric seasonal 356 xvi Contents of Volume 1

5.2. Reduced form 357 5.3. Nowcasting 358 5.4. Holt–Winters 358 5.5. Seasonal ARIMA models 358 5.6. Extensions 360 6. State space form 361 6.1. Kalman filter 361 6.2. Prediction 363 6.3. Innovations 364 6.4. Time-invariant models 364 6.5. Maximum likelihood estimation and the prediction error decomposition 368 6.6. Missing observations, temporal aggregation and mixed frequency 369 6.7. Bayesian methods 369 7. Multivariate models 370 7.1. Seemingly unrelated times series equation models 370 7.2. Reduced form and multivariate ARIMA models 371 7.3. Dynamic common factors 372 7.4. Convergence 376 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 1. 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 2.4. Switching regression and threshold autoregressive model 420 2.5. Markov-switching model 421 2.6. Artificial neural network model 422 2.7. Time-varying regression model 423 2.8. Nonlinear moving average models 424 3. Building nonlinear models 425 3.1. Testing linearity 426 3.2. Building STR models 428 3.3. Building switching regression models 429 3.4. Building Markov-switching regression models 431 4. Forecasting with nonlinear models 431 4.1. Analytical point forecasts 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 4.6. Combining forecasts 438 4.7. Different models for different forecast horizons? 439 5. Forecast accuracy 440 5.1. Comparing point forecasts 440 6. Lessons from a simulation study 4 7. Empirical forecast comparisons 445 7.1. Relevant issues 445 7.2. Comparing linear and nonlinear models 447 7.3. Large forecast comparisons 448 8. Final remarks 451 Acknowledgements 452 References 453

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

(Parte 1 de 5)

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