I-22 Subject Index Federal Reserve Board 749 feedback 704 FIEGARCH 806 filter 799 filtering 814, 882 filtering problem 782 final equations form 311 financial risk management 203 financial time series 662 first order term 565 fixed scheme 107 fixed-weighted data 971 flexible Fourier form 698 forecast biases 620 forecast combination 23, 141, 438, 520, 864 forecast combination puzzle 186 forecast comparisons 416 forecast distributions 809 forecast efficiency 975 forecast encompassing 101, 109, 157 forecast errors 101, 611, 975 forecast evaluation 101, 106, 782, 786, 855 forecast horizon 843, 937 forecast loss function 787, 854 forecast MSE 296, 462 forecast performance 610 forecast pooling 883 forecast quality 785 forecast-equivalent labeling 92 forecast-origin 613 forecast-origin inaccuracy 611 forecasting aggregated processes 299 forecasting competitions 607 forecasting conditional covariances and correla- tions 786 forecasting “horse race” 52 forecasting performance 883, 934 forecasting vector of interest 9 forecasting volatility 854 forecasting with estimated processes 316 forward premium 592 fractional integrated EGARCH 806 fractional integration 59 fractionally integrated FIGARCH 805 frequentist formulation 23 fully efficient forecasts 786 GARCH 111, 405, 615, 782 GARCH volatility 798 GARCH(1, 1) model 696 GDP 881 generalized error distribution 813 generically comprehensively revealing activation functions 475 Gibbs sampler 31, 826 GMM 112 Goldsmith–Nagan Bond and Money Market Let- ter 736, 758 Gompertz function 999 Granger causality 301 Granger causality tests 976 greedy algorithm 472 gross national product 884 growth or deviation cycle 881 GW test 443 “h-block” cross-validation 482 heavy-tailed distributions 399 hedging problem 67 heterogeneity 716 heterogeneous information 722 hidden Markov regression model 421 hierarchical Bayes 1002 hierarchical prior 11, 12 high-frequency data 786, 830 higher order integrated process 305 highest density region 438 highly nonlinear approximation 471 hold-out sample 494 Holt–Winters procedure 358 h step ahead forecast 565 “hv-block” cross-validation 482 hyperbolic tangent function 418 hyperparameters 12 IFO 751, 764 IGARCH 800 impact parameter 584 implied volatility 780, 838 importance sampling 25, 29 impulse response functions 1005 in-sample forecasts 977 index of leading indicators 963 industrial production 881, 884 inflation expectations 730 inflation forecasting 63 inflection point 992 information criteria 520, 896, 974 information set 782 initial condition 563 innovation outlier 625 innovations 364 INSÉE 747 Subject Index I-23 instantaneous elasticity 998 Institut für Wirtschaftsforschung 735 Institute of Supply Management survey 735 integrated GARCH 800 integrated process 290, 905 integrated variance 784, 795 integrated volatility 784, 795 integration by Arnold Zellner 43 intercept corrections 633 interpreting approximation-based forecasts 485 interpreting linear forecasts 484 interpreting nonlinear forecasts 490 interval forecast 438, 788, 859, 860 intervention variables 354 intra-daily seasonality 696 invertibility 425 invertibility condition for the MA operator 293 Iowa Economic Forecast 68 Italy’s Survey of Household Income and Wealth 736 Japan Centre for International Finance 760 Joseph Livingston 735 jump 818 jump component 835 Kalman filter 43, 362, 821, 895, 978 Kalman smoother 895 kernel 27 kernel density estimator 201 Kolmogorov 203 Kolmogorov–Smirnov test 202 Koyck model 993, 994 Koyck transformation 994 Kronecker indices 308 Kuipers Score 85 Kullback–Leibler Information Criterion (KLIC) 205 Lagrange multiplier 427 latent class 1002 latent variables 8, 814 latent volatility process 820 latest-available data 970 latest-available forecasts 972 LDGP 608 leading indicators 54, 382, 881 left-coprime operator 307 level shifts 625 leverage effects 11, 803 likelihood function 8, 846 likelihood ratio tests 314 limiting distribution 203 Lin-Lin 731, 732, 758, 759 linear forecasts 289 linear models 289 linear parametric model 463 linear transformations of VARMA process 294 LINEX 731, 732 Litterman prior 46 Livingston Survey 735, 736, 748, 750 Ljung–Box statistics 863 local DGP 608 local level model 337 local linear trend 339 local power 560 local to unity 560 location shifts 620 location-dependent error-based form 96 log probability score 935 log-likelihood function of VARMA model 311 logical consistency 17, 1004 logistic function 418, 928, 999 logistic STR model 419 logit 890, 993 long horizon 565, 579 long horizon forecasts 125 long memory 12, 59, 805 long run models 681 long run variance 113 loss function 20, 83, 93, 103, 104, 141, 447, 897 marginal likelihood 15 marginal process 295 marginalization 10 market microstructure frictions 853 market share attraction model 997 market shares 986, 988 market timing tests 860 marketing activities 985 marketing-mix 987 Markov chain 421, 890 Markov chain Monte Carlo (MCMC) 30, 826 Markov chain Monte Carlo model composition 539 Markov-switching model (MS) 421, 636, 693, 882 martingale difference 120, 721 martingale processes 756, 757 martingalization 204 matrix Student-t 42 maximum likelihood 112, 200, 910 I-24 Subject Index Maximum Likelihood Estimation 807 MDH 815 mean absolute error 109, 440, 935 mean absolute prediction error 101, 104, 110 mean prediction error 104, 109 mean square error 205, 559, 895 mean square forecast error 13, 101, 424, 663, 935 mean squared error (MSE) loss 88, 142 mean utility or profit 104 measures of performance 104 Method of Simulated Moments (MSM) 823 methods of moments 200 Metropolis independence chain 33 Metropolis random walk 33 Metropolis within Gibbs 34 Metropolis–Hastings algorithm 33 Michigan Survey 734, 754, 760, 761, 763, 765, 766 Mincer–Zarnowitz volatility regression 856 minimum MSE forecast 296 Minneapolis Fed model 69 “Minnesota” prior 45 missing observations 369, 883 misspecification bias 138 misspecification test 429 misspecified models 462, 481 misspecified seasonal models 672 mixed estimator 47 mixed normal distribution 594 mixture model 816 mixture model for time-variation in the combina- tion weights 168 mixture of distributions hypothesis 815 model instability 154 model selection 200, 481, 977 model selection criteria 430 model specification 782, 815 moment matching 821 momentum-TAR model 420 monetary policy 705 Monetary Policy Committee 737 Money Market Services Inc. 755 Monte Carlo 570, 637, 811, 974 Monte Carlo forecast 434 MSPE-adjustment 121 multi-level regression model 993 multicollinearity 44 multinomial logit 993 multinomial probit 993 multiple structural break 623 multistep predictions 118, 200, 416 multivariate 600, 786 multivariate GARCH 841 multivariate innovations algorithm 297 multivariate normal 12 multivariate stochastic volatility 847 multivariate Student-t density 42 multivariate volatility 839 National Association of Business Economists 736 National Association of Purchasing Managers’ Surveys 752 national income account data 974 NBER 895 nearly nonstationary model 560 nested models 102, 117 Netherlands’ Socio-Economic Panel 765 Netherlands’ VSB Panel Survey 736 neural networks 170, 416, 883 new product diffusion 989, 991 new product introduction 986 nonlinear approximations 469 nonlinear combination 165, 169 nonlinear dynamic regression model 417 nonlinear forecasting 416 nonlinear least squares 467, 493, 502 nonlinear model 117, 200, 416, 635, 691, 886, 985 nonlinear model building 417 nonlinear moving average model 424 nonlinear parametric model 466 nonlinearities 391 nonnested model 104, 123 nonnormal 119, 306 nonparametric 117 nonparametric combination 160 nonparametric empirical Bayes 544 nonparametric forecasting 416 nonrejection 18 nonstationarity 560, 647 “normal-diffuse” prior 51 normal-gamma posterior 41 normal-Wishart 50 normal-Wishart sampling 71 ‘nowcasting’ 340 nuisance parameters 204, 563 numerical integration 6 numerical solutions 637 numerical standard error 29 Subject Index I-25 objective function 88 observed transition model 883 one step ahead prediction error 107 one-step-ahead forecasts 54 optic scanner data 985 optimal action function 89 optimal combination 141, 521 optimal forecast 788, 854 optimal hedging strategy 67 optimal linear approximation 463 optimal nonlinear approximation 466 optimal point forecast 467 option valuation 794 order of integration 305 ordered regression model 993 ordinary least squares estimator 465 orthogonality condition 112, 728 orthogonality regression 598 out-of-sample forecast error 598 out-of-sample forecasting 827, 977 outliers 400, 625, 882 output gap 976 overall tightness 47 overfit 480 overidentified 112 Panel Survey of Income Dynamics 750 panels of time series 993 PAR (periodic autoregressive) models 683 parameter constancy 608, 909 parameter estimation error 131, 202 parameter fluctuation test 624 parameter instability 623 parameter-estimation uncertainty 609 parameterization 463, 466, 468, 474 parametric empirical Bayes 544 parametric rate 201 particle filter 827 pattern recognition algorithm 929 PCA: large-n theoretical results 529 peak 881 periodic cointegration 688 periodic GARCH model 700 periodic integration 684 periodic model 360, 683 periodic process 304 periodic stochastic volatility model 701 permanent shifts 625 persistence in the performance of forecasting models 184 Philadelphia Fed’s Survey of Professional Fore- casters 736 Phillips curve 976 piecewise linear model 420 pivotal test statistic 18 plug-in principle 467 point expectations 720 point forecast 37, 83, 200, 431, 787 point-forecast equivalent 90 point-forecast/point-realization loss function 89 point-in-time sampling 302 polynomials 500 pooling 635 pooling information 143 portfolio allocations 10 portfolio diversification 137 portfolio weights 839 posterior density 16 posterior distribution 11 posterior odds ratio 15 posterior pdf 907 posterior predictive distributions 17 posterior probability 15, 205 posterior simulation 25 power 123, 204 predictability 966 predicting business cycle phases 883 prediction error decomposition 368 predictive Bayes factor 16 predictive conditional distributions 200 predictive density 16 predictive density evaluation 200 predictive inference 103 predictive intervals 38 predictive least squares 933 predictive likelihood 16 predictive pdf 907 price elasticities 1001 prices 985 pricing strategies 986 principal components analysis 528 prior distribution 10 prior information 6 prior odds ratio 15 prior predictive density 11 probability and duration forecasts 951 probability approach 739 probability density forecasts 176 probability density function 8 probability forecast evaluation 860 I-26 Subject Index probability forecasting 22, 788 probability integral transform 22, 202 probability integral transform (PIT) 861 probability limits 201 probability of transition 899 probit model 890, 993 projection pursuit 446 promotional activities 986 propagation mechanism 951 QMLE 808 quadratic probability score 935 qualitative data 395, 753, 763 qualitative questions 734 qualitative responses 728 qualitative survey data 739 qualitative surveys 751 quantile predictions 810 questionnaires 986 QuickNet 476, 478, 497, 503 radial basis function 423, 472 random walk 623 rank condition 117 Rao–Blackwellization 27 rational expectations hypothesis 721 RATS 69 real-time data 962 real-time data setfor macroeconomists (RTDSM) 965 real-time forecasting 40, 624, 972 real-time information 883 reality check 130 realized covariances and correlations 849, 850 realized covariation 849, 850 realized volatility 783, 786, 795, 830 realized volatility errors 849 realized volatility forecasting 835 realized volatility modeling 834 recession 640, 963 recession indicator 911 recursive forecasting 433, 972 recursive formulation 19 recursive scheme 106 regime switching type models 851 regional forecasting 64 regression based tests 116 regression parameters 106 REH 727–729, 757 relative numerical efficiency 29 relaxed greedy algorithm 472, 478 relevant conditioning 7 repeated observation forecasting 971 residual adjustments 633 retrospective fluctuation test 624 return variability 818 return variance 818 return volatility 780 reversibility condition 34 revision 881 revision process 966 reweighting 40 ridge regression 13, 45 ridgelets 472, 498 risk 561 risk management 790 RiskMetrics 798, 840 rolling regressions 107, 798 rolling sample windows 798 root mean square error 55 root mean square forecast error 440 RR regression 312 S&P 500 index 492 sales 986 sample survey error 343 sampling frequency 836 SARIMA model 665 SARV 817 scalar component models 311 SCAN*PRO 1005 Schwarz information criterion 318, 685, 971 seasonal adjustment 662, 882, 967 seasonal ARIMA models 359 seasonal cointegration 677 seasonal component 355 seasonal differencing 666 seasonal dummies 670 seasonal heteroskedasticity 696 seasonal process 303 seasonal random walk 672 seasonal unit roots 305, 667 seasonality 662 seasonality in variance 696 seasonally integrated model 666 seemingly unrelated times series equation (SUTSE) models 47, 370 segmentation 1002 self-exciting threshold autoregressive model(SE- TAR) 418, 636 semi-martingale 832 semi-parametric models 200 sequential test bias 202 Subject Index I-27 serial correlation 567, 863 series functions 468 shrinkage 11, 170, 184, 185 shrinkage forecast 522 sign forecasting 788 similar cycle 370 simple combination forecast 155, 522 simulated annealing 423 simulated moments, Markov Chain Monte Carlo (MCMC) 814 simulation based method 905, 985 simulation error 825 simulation-consistency 26 simulation-consistent approximation 40 simultaneous-equations model 112, 117, 975 skip-sampling 302 smooth transition autoregressive (STAR) model 416, 420, 692 smooth transition model 927 smooth transition regression model 418 smoothing 814 smoothing parameter 927 smoothness 470 source density 27 sources of forecast error 609–612 specification testing 200, 202 specifying Kronecker indices 314 specifying lag orders 314 “Spectre” 69 spot volatility 783 spurious regression 596 squared returns 784 stable process 293 state space 821, 895, 978 state space form 361 state space mixture models 14 state space observer system 43 state variable 912 stationarity 102 stationary linear models 56 statistical decision theory 84 statistical decisions 87 stochastic autoregressive volatility 817 stochastic cycle 344 stochastic differential equation 783 stochastic discount factor 792 stochastic random coefficient model 424 stochastic trend 335 stochastic volatility 9, 404, 786, 794, 814 stochastic volatility models 782 structural breaks 138, 154, 400, 607 structural change model 607 structural time series models 331 Student-t distribution 12 subjective uncertainty 749 suddenly changing autoregressive model 421 survey data 716, 986 Survey of Blue Chip Forecasters 736 Survey of Consumer Expectations 734 Survey of Household Income and Wealth 749 Survey of Professional Forecasters 186, 729, 733, 736, 749, 750, 759–761, 767, 965 switching regression model 419 systematic sampling 302 “take-off” point 992 Tankan 735 target density 33 target variable 881 taxonomy of forecast errors 607 temporal aggregation 295, 302, 995 term-structure-of-variance 801 test of conditional forecasting ability 442 testing cointegrating rank 313 testing for nonlinearity 636 testing linearity 425 tests for structural change 622 tests of rational expectations 716 TGARCH 803 Theil’s U 48 thick modeling 163, 425 threshold autoregressive (TAR) model 692 Threshold GARCH 803 threshold model 692 time consistency 728 time series models 993 time trend 567 time-variation in forecast combination weights 165 time-varying betas 792 time-varying coefficients 623 time-varying covariance 793, 840 time-varying parameters 168, 355, 523, 883 time-varying regression model 423 transition density 33 transition equation 822 transition function 419, 927 transition probability 421 trending regressors 562 trimming 162, 183, 185 trimming of forecasts 449 trough 881 true model 18 I-28 Subject Index turning point 881 two-stage-least-squares 974 U.S. Health and Retirement Survey 736 U.S. Survey of Consumers 736 U.S. Survey of Economic Expectations 736 uncertainty 780 unconditional expected loss 574 unidentified parameter 623 uniform random variable 203 unimodular operator 307 unit root 12 unit root model 622 unit root pretesting 570 univariate model 563 univariate volatility forecasting 786 universal approximator 423 University of Wisconsin’s Survey of Economic Expectations 749 unobserved components models 662 unobserved heterogeneity 1002 updating 630 utility function 83 Value-at-Risk 200, 790, 854 Value-at-Risk evaluation 859 VAR in differences (DVAR) 618 variable transformation 881 VARMA 58, 292 VA RM A (p, q) process 292 vech model 844 VECM 289, 294, 617 vector autoregression 8, 11, 289, 558, 612–614, 901, 993 vector autoregressive moving-average (VARMA) models 289 volatility 780 volatility dynamics 789 “volatility feedback” effect 803 volatility forecast evaluation 855 volatility forecasting 416, 781, 796 volatility impulse response function 806 volatility modeling 781 volatility process 782 volatility proxy 857 volatility signature plot 858 Wald test 427 wavelets 469 weakly stationary 901 web-based surveys 985 weekly, daily or hourly observations 360 weighted average 23 weighted principal components 530 weighting scheme 882, 892 Wharton Econometric Forecasting Associates 69 Wiener 780 Wishart random matrix 50 Wold MA representation 293 Wolf’s sunspot numbers 446 X-11 method 702 X-12-ARIMA 702 HANDBOOKS IN ECONOMICS 1. 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