TAILIEUCHUNG - Handbook of Economic Forecasting part 104

Handbook of Economic Forecasting part 104. 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 | 1004 PH. Franses closed-form solutions to these expressions and hence one has to resort to simulationbased techniques. In this section the focus will be on the attraction model and on the Bass model where the expressions for out-of-sample forecasts will be given. Additionally there will be a discussion of how one should derive forecasts for market shares when forecasts for sales are available. . Attraction model forecasts As discussed earlier the attraction model ensures logical consistency that is market shares lie between 0 and 1 and they sum to 1. These restrictions imply that functions of model parameters can be estimated from a multivariate reduced-form model with I 1 equations. The dependent variable in each of the I 1 equations is the natural logarithm of a relative market share that is log mi t log Mf- for i 1 2 . . . I 1 where the base brand I can be chosen arbitrarily as discussed before. In practice one is usually interested in predicting Mi t and not in forecasting the logs of the relative market shares. Again it is important to recognize that first of all exp E log mi t is not equal to E mi t and that secondly E MF is not equal to EMFJ. MI t E MI t J Therefore unbiased market share forecasts cannot be directly obtained by these data transformations. To forecast the market share of brand i at time t one needs to consider the relative market shares Mjt mj t - for j 1 2 . I 48 MI t as m1 t . mI 1 t form the dependent variables after log transformation in the reduced-form model. As MI t 1 2 j 1 Mj t it holds that mi t Mi t -AA-------- for i 1 2 . I. 49 Ej 1 mJ t Fok Franses and Paap 2002 propose to simulate the one-step ahead forecasts of the market shares as follows. First draw n from N 0 Ë then compute I K m l ex .i l x k J i 50 mi t exV Ai ni t xk j t 50 with m j 1 and finally compute l m M l ------ ----- for i 1 i 51 it I l or . . . Ej 1 mJ t where l 1 . L denotes the simulation iteration. Each vector mF. Mf. gen-1 t I t erated this way is a draw .

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