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Handbook of Economic Forecasting part 46

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Handbook of Economic Forecasting part 46. Research on forecasting methods has made important progress over recent years and these developments are brought together in the Handbook of Economic Forecasting. The handbook covers developments in how forecasts are constructed based on multivariate time-series models, dynamic factor models, nonlinear models and combination methods. The handbook also includes chapters on forecast evaluation, including evaluation of point forecasts and probability forecasts and contains chapters on survey forecasts and volatility forecasts. Areas of applications of forecasts covered in the handbook include economics, finance and marketing | 424 T. Terâsvirta where the transition function G y c st 1 exp 2L - y O i -Ck -i y 0. 13 When K 1 and y œ in 13 Equation 12 represents a linear dynamic regression model with a break in parameters at t c1.Itcanbe generalized to a model with several transitions yt 4 xt Gj ZtGj .yj Cj t t t 1 . T 14 where transition functions Gj typically have the form 13 with K 1. When yj j 1 . r in 14 the model becomes a linear model with multiple breaks. Specifying such models has recently received plenty of attention see for example Bai and Perron 1998 2003 and Banerjee and Urga 2005 . In principle these models should be preferable to linear models without breaks because the forecasts are generated from the most recent specification instead of an average one which is the case if the breaks are ignored. In practice the number of break-points and their locations have to be estimated from the data which makes this suggestion less straightforward. Even if this difficulty is ignored it may be optimal to use pre-break observations in forecasting. The reason is that while the one-step-ahead forecast based on post-break data is unbiased if the model is correctly specified it may have a large variance. The mean square error of the forecast may be reduced if the model is estimated by using at least some pre-break observations as well. This introduces bias but at the same time reduces the variance. For more information of this bias-variance trade-off see Pesaran and Timmermann 2002 . Time-varying coefficients can also be stochastic yt t zt t t 1 . T 15 where t is a sequence of random variables. In a large forecasting study Marcellino 2002 assumed that t was a random walk that is A0t was a sequence of normal independent variables with zero mean and a known variance. This assumption is a testable alternative to parameter constancy see Nyblom 1989 . For the estimation of stochastic random coefficient models the reader is referred to Harvey 2006 . Another assumption albeit a less popular one in