Handbook of Economic Forecasting part 20. 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 | 164 A. Timmermann Then the first term on the right-hand side of 41 is given by BE f B De bibl 0 0 b2bi 0 42 0 0 . 0 0 D 1 De 0 bnf b nfJ where DaF is a diagonal matrix with af in its first n1 diagonal places followed by af in the next n2 diagonal places and so on and De is a diagonal matrix with Var e t as the th diagonal element. Thus the matrix in 42 and its inverse will be block diagonal. Provided that the forecasts tracking the individual factors can be grouped and have similar factor exposure b within each group this suggests that little is lost by pooling forecasts within each cluster and ignoring correlations across clusters. In a subsequent step sample counterparts of the optimal combination weights for the grouped forecasts can be obtained by least-squares estimation. In this way far fewer combination weights n f rather than N have to be estimated. This can be expected to decrease forecast errors and thus improve forecasting performance. Building on these ideas Aiolfi and Timmermann 2006 propose to sort forecasting models into clusters using a K-mean clustering algorithm based on their past MSE performance. As the previous argument suggests one could alternatively base clustering on correlation patterns among the forecast Their method identifies K clusters. Let yk h t be the pk x 1 vector containing the subset of forecasts belonging to cluster k k 1 2 . K .By ordering the clusters such that the first cluster contains models with the lowest historical MSE values Aiolfi and Timmermann consider three separate strategies. The first simply computes the average forecast across models in the cluster of previous best models h A P1 y1 h t. 43 A second combination strategy identifies a small number of clusters pools forecasts within each cluster and then estimates optimal weights on these pooled predictions by least squares _ . yt h t t h tA Ak pt 44 where a t h t k are least-squares estimates of the optimal combination weights for the K clusters. This .
