TAILIEUCHUNG - Handbook of Economic Forecasting part 47

Handbook of Economic Forecasting part 47. 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 | 434 T Terasvirta where nt n1t nkt iid 0 En . The one-step-ahead forecast of xt 1 is xt i t Axt. This yields yt 2 t E y 2 xt Eg Ax nt 1 6 g Axt nt i 6 dF m . nk 31 ni nk which is a k-fold integral and where F n1 nk is the joint cumulative distribution function of nt. Even in the simple case where xt yt yt-p 1 one has to integrate out the error term et from the expected value E yt 2 xt . It is possible however to ignore the error term and just use yt 2 t g xt 1 t 6 which Tong 1990 calls the skeleton forecast. This method while easy to apply yields however a biased forecast for yt 2. It may lead to substantial losses of efficiency see Lin and Granger 1994 for simulation evidence of this. On the other hand numerical integration of 31 is tedious. Granger and Terasvirta 1993 call this method of obtaining the forecast the exact method as opposed to two numerical techniques that can be used to approximate the integral in 31 . One of them is based on simulation the other one on bootstrapping the residuals nt of the estimated equation 30 or the residuals et of the estimated model 29 in the univariate case. In the latter case the parameter estimates thus do have a role to play but the additional uncertainty of the forecasts arising from the estimation of the model is not accounted for. The simulation approach requires that a distributional assumption is made about the errors nt. One draws a sample of N independent error vectors nt 1 n 1 from this distribution and computes the Monte Carlo forecast ytw 1 N xt nt n 6 32 The bootstrap forecast is similar to 32 and has the form yf 2 t 1 Nb xt 1 t n 1 6 33 aazTazaa za -Taza t C i B i 1 Taoazza Tazazaaa zATA orrAZAz- Taaz zl rm r aa za Tazaaaa 4a zaaaa Taza cza where me errors n 1 nt 1 have oeen obtained oy drawing mem from me set of estimated residuals of model 30 with replacement. The difference between 32 and 33 is that the former is based on an assumption about the distribution of nt 1 whereas the latter does not make use of a .

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