tailieunhanh - Handbook of Economic Forecasting part 60

Handbook of Economic Forecasting part 60. 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 | 564 G. Elliott n W s for y 0 T-1 2 u Ts oiM s . 2 ae-YS 2y -1 2 vf e-Y s-V dW else where IT - is a standard univariate Brownian motion. Also note that for y 0 MG 2 a2e-2YS 2y 1 - e-2YS 2y a2 - 1 e-2YS 2y 1 2y which will be used for approximating the MSE below. If we knew that p 1 then the variable has a unit root and forecasting would proceed using the model in first differences following the Box and Jenkins 1970 approach. The idea that we know there is an exact unit root in a data series is not really relevant in practice. Theory rarely suggests a unit root in a data series and even when we can obtain theoretical justification for a unit root it is typically a special case model examples include the Hall 1978 model for consumption being a random walk also results that suggest stock prices are random walks . For most applications a potentially more reasonable approach both empirically and theoretically would be to consider models where p 1 and there is uncertainty over its exact value. Thus there will be a tradeoff between gains of imposing the unit root when it is close to being true and gains to estimation when we are away from this range of models. A first step in considering how to forecast in this situation is to consider the cost of treating near unit root variables as though they have unit roots for the purposes of forecasting. To make any headway analytically we must simplify dramatically the models to show the effects. We first remove serial correlation. In the case of the model in 1 and c L 1 yT h - yT T h PST h-1 -- ph-1 T 1 p - 1 yT - ftZt ZT h - Zt Jh . ph 1 St i p - 1 yT - Zt ZT h - Zt - i 1 Given that largest root p describes the stochastic trend in the data it seems reasonable that the effects will depend on the forecast horizon. In the short run mistakes in estimating the trend will differ greatly from when we forecast further into the future. As this is the case we will take these two sets of horizons separately. A number of papers have examined .