Handbook of Economic Forecasting part 3 pps

xx Contents of Volume 1 3.2. GARCH model forecast-error taxonomy 616 4. Forecasting when there are breaks 617 4.1. Cointegrated vector autoregressions 617 4.2. VECM forecast errors 618 4.3. DVAR forecast errors 620 4.4. Forecast biases under location shifts 620 4.5. Forecast biases when there are changes in the autoregressive parameters 621 4.6. Univariate models 622 5. Detection of breaks 622 5.1. Tests for structural change 622 5.2. Testing for level shifts in ARMA models 625 6. Model estimation and specification 627 6.1. Determination of estimation sample for a fixed specification 627 6.2. Updating 630 7. Ad hoc forecasting devices 631 7.1. Exponential smoothing 631 7.2. Intercept corrections 633 7.3. Differencing 634 7.4. Pooling 635 8. Non-linear models 635 8.1. Testing for non-linearity and structural change 636 8.2. Non-linear model forecasts 637 8.3. Empirical evidence 639 9. Forecasting UK unemployment after three crises 640 9.1. Forecasting 1992–2001 643 9.2. Forecasting 1919–1938 645 9.3. Forecasting 1948–1967 645 9.4. Forecasting 1975–1994 647 9.5. Overview 647 10. Concluding remarks 648 Appendix A: Taxonomy derivations for Equation (10) 648 Appendix B: Derivations for Section 4.3 650 References 651 Chapter 13 Forecasting Seasonal Time Series ERIC GHYSELS, DENISE R. OSBORN AND PAULO M.M. RODRIGUES 659 Abstract 660 Keywords 661 1. Introduction 662 2. Linear models 664 2.1. SARIMA model 664 2.2. Seasonally integrated model 666 Contents of Volume 1 xxi 2.3. Deterministic seasonality model 669 2.4. Forecasting with misspecified seasonal models 672 2.5. Seasonal cointegration 677 2.6. Merging short- and long-run forecasts 681 3. Periodic models 683 3.1. Overview of PAR models 683 3.2. Modelling procedure 685 3.3. Forecasting with univariate PAR models 686 3.4. Forecasting with misspecified models 688 3.5. Periodic cointegration 688 3.6. Empirical forecast comparisons 690 4. Other specifications 691 4.1. Nonlinear models 691 4.2. Seasonality in variance 696 5. Forecasting, seasonal adjustment and feedback 701 5.1. Seasonal adjustment and forecasting 702 5.2. Forecasting and seasonal adjustment 703 5.3. Seasonal adjustment and feedback 704 6. Conclusion 705 References 706 PART 4: APPLICATIONS OF FORECASTING METHODS Chapter 14 Survey Expectations M. HASHEM PESARAN AND MARTIN WEALE 715 Abstract 716 Keywords 716 1. Introduction 717 2. Concepts and models of expectations formation 720 2.1. The rational expectations hypothesis 721 2.2. Extrapolative models of expectations formation 724 2.3. Testable implications of expectations formation models 727 2.4. Testing the optimality of survey forecasts under asymmetric losses 730 3. Measurement of expectations: History and developments 733 3.1. Quantification and analysis of qualitative survey data 739 3.2. Measurement of expectations uncertainty 744 3.3. Analysis of individual responses 745 4. Uses of survey data in forecasting 748 4.1. Forecast combination 749 4.2. Indicating uncertainty 749 4.3. Aggregated data from qualitative surveys 751 5. Uses of survey data in testing theories: Evidence on rationality of expectations 754 xxii Contents of Volume 1 5.1. Analysis of quantified surveys, econometric issues and findings 755 5.2. Analysis of disaggregate qualitative data 764 6. Conclusions 767 Acknowledgements 768 Appendix A: Derivation of optimal forecasts under a ‘Lin-Lin’ cost function 768 Appendix B: References to the main sources of expectational data 769 References 770 Chapter 15 Volatility and Correlation Forecasting TORBEN G. ANDERSEN, TIM BOLLERSLEV, PETER F. CHRISTOFFER- SEN AND FRANCIS X. DIEBOLD 777 Abstract 779 Keywords 779 1. Introduction 780 1.1. Basic notation and notions of volatility 781 1.2. Final introductory remarks 786 2. Uses of volatility forecasts 786 2.1. Generic forecasting applications 787 2.2. Financial applications 789 2.3. Volatility forecasting in fields outside finance 796 2.4. Further reading 797 3. GARCH volatility 798 3.1. Rolling regressions and RiskMetrics 798 3.2. GARCH(1, 1) 800 3.3. Asymmetries and “leverage” effects 803 3.4. Long memory and component structures 805 3.5. Parameter estimation 807 3.6. Fat tails and multi-period forecast distributions 809 3.7. Further reading 812 4. Stochastic volatility 814 4.1. Model specification 815 4.2. Efficient method of simulated moments procedures for inference and forecasting 823 4.3. Markov Chain Monte Carlo (MCMC) procedures for inference and forecasting 826 4.4. Further reading 828 5. Realized volatility 830 5.1. The notion of realized volatility 830 5.2. Realized volatility modeling 834 5.3. Realized volatility forecasting 835 5.4. Further reading 837 6. Multivariate volatility and correlation 839 6.1. Exponential smoothing and RiskMetrics 840 6.2. Multivariate GARCH models 841 Contents of Volume 1 xxiii 6.3. Multivariate GARCH estimation 843 6.4. Dynamic conditional correlations 845 6.5. Multivariate stochastic volatility and factor models 847 6.6. Realized covariances and correlations 849 6.7. Further reading 851 7. Evaluating volatility forecasts 853 7.1. Point forecast evaluation from general loss functions 854 7.2. Volatility forecast evaluation 855 7.3. Interval forecast and Value-at-Risk evaluation 859 7.4. Probability forecast evaluation and market timing tests 860 7.5. Density forecast evaluation 861 7.6. Further reading 863 8. Concluding remarks 864 References 865 Chapter 16 Leading Indicators MASSIMILIANO MARCELLINO 879 Abstract 880 Keywords 880 1. Introduction 881 2. Selection of the target and leading variables 884 2.1. Choice of target variable 884 2.2. Choice of leading variables 885 3. Filtering and dating procedures 887 4. Construction of nonmodel based composite indexes 892 5. Construction of model based composite coincident indexes 894 5.1. Factor based CCI 894 5.2. Markov switching based CCI 897 6. Construction of model based composite leading indexes 901 6.1. VAR based CLI 901 6.2. Factor based CLI 908 6.3. Markov switching based CLI 912 7. Examples of composite coincident and leading indexes 915 7.1. Alternative CCIs for the US 915 7.2. Alternative CLIs for the US 918 8. Other approaches for prediction with leading indicators 925 8.1. Observed transition models 925 8.2. Neural networks and nonparametric methods 927 8.3. Binary models 930 8.4. Pooling 933 9. Evaluation of leading indicators 934 9.1. Methodology 934 xxiv Contents of Volume 1 9.2. Examples 937 10. Review of the recent literature on the performance of leading indicators 945 10.1. The performance of the new models with real time data 946 10.2. Financial variables as leading indicators 947 10.3. The 1990–1991 and 2001 US recessions 949 11. What have we learned? 951 References 952 Chapter 17 Forecasting with Real-Time Macroeconomic Data DEAN CROUSHORE 961 Abstract 962 Keywords 962 1. An illustrative example: The index of leading indicators 963 2. The real-time data set for macroeconomists 964 How big are data revisions? 967 3. Why are forecasts affected by data revisions? 969 Experiment 1: Repeated observation forecasting 971 Experiment 2: Forecasting with real-time versus latest-available data samples 972 Experiment 3: Information criteria and forecasts 974 4. The literature on how data revisions affect forecasts 974 How forecasts differ when using first-available data compared with latest-available data 974 Levels versus growth rates 976 Model selection and specification 977 Evidence on the predictive content of variables 978 5. Optimal forecasting when data are subject to revision 978 6. Summary and suggestions for further research 980 References 981 Chapter 18 Forecasting in Marketing PHILIP HANS FRANSES 983 Abstract 984 Keywords 984 1. Introduction 985 2. Performance measures 986 2.1. What do typical marketing data sets look like? 986 2.2. What does one want to forecast? 991 3. Models typical to marketing 992 3.1. Dynamic effects of advertising 993 3.2. The attraction model for market shares 997 3.3. The Bass model for adoptions of new products 999 3.4. Multi-level models for panels of time series 1001 Contents of Volume 1 xxv 4. Deriving forecasts 1003 4.1. Attraction model forecasts 1004 4.2. Forecasting market shares from models for sales 1005 4.3. Bass model forecasts 1006 4.4. Forecasting duration data 1008 5. Conclusion 1009 References 1010 Author Index I-1 Subject Index I-19 This page intentionally left blank PART 1 FORECASTING METHODOLOGY This page intentionally left blank Chapter 1 BAYESIAN FORECASTING JOHN GEWEKE and CHARLES WHITEMAN Department of Economics, University of Iowa, Iowa City, IA 52242-1000 Contents Abstract 4 Keywords 4 1. Introduction 6 2. Bayesian inference and forecasting: A primer 7 2.1. Models for observables 7 2.1.1. An example: Vector autoregressions 8 2.1.2. An example: Stochastic volatility 9 2.1.3. The forecasting vector of interest 9 2.2. Model completion with prior distributions 10 2.2.1. The role of the prior 10 2.2.2. Prior predictive distributions 11 2.2.3. Hierarchical priors and shrinkage 12 2.2.4. Latent variables 13 2.3. Model combination and evaluation 14 2.3.1. Models and probability 15 2.3.2. A model is as good as its predictions 15 2.3.3. Posterior predictive distributions 17 2.4. Forecasting 19 2.4.1. Loss functions and the subjective decision maker 20 2.4.2. Probability forecasting and remote clients 22 2.4.3. Forecasts from a combination of models 23 2.4.4. Conditional forecasting 24 3. Posterior simulation methods 25 3.1. Simulation methods before 1990 25 3.1.1. Direct sampling 26 3.1.2. Acceptance sampling 27 3.1.3. Importance sampling 29 3.2. Markov chain Monte Carlo 30 3.2.1. The Gibbs sampler 31 Handbook of Economic Forecasting, Volume 1 Edited by Graham Elliott, Clive W.J. Granger and Allan Timmermann © 2006 Elsevier B.V. All rights reserved DOI: 10.1016/S1574-0706(05)01001-3 . 6 83 3.1. Overview of PAR models 6 83 3.2. Modelling procedure 685 3. 3. Forecasting with univariate PAR models 686 3. 4. Forecasting with misspecified models 688 3. 5. Periodic cointegration 688 3. 6 developments 733 3. 1. Quantification and analysis of qualitative survey data 739 3. 2. Measurement of expectations uncertainty 744 3. 3. Analysis of individual responses 745 4. Uses of survey data in forecasting. 636 8.2. Non-linear model forecasts 637 8 .3. Empirical evidence 639 9. Forecasting UK unemployment after three crises 640 9.1. Forecasting 1992–2001 6 43 9.2. Forecasting 1919–1 938 645 9 .3. Forecasting