tailieunhanh - Handbook of Economic Forecasting part 53

Handbook of Economic Forecasting part 53. 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 | 494 H. White using this last step but also because it facilitates a feasible computation of an approximation to the cross-validated MSE. Although we touched on this issue only briefly above it is now necessary to confront head-on the challenges for cross-validation posed by models nonlinear in the parameters. This challenge is that in order to compute exactly the cross-validated MSE associated with any given nonlinear model one must compute the NLS parameter estimates obtained by holding out each required validation block of observations. There are roughly as many validation blocks as there are observations thousands here . This multiplies by the number of validation blocks the difficulties presented by the convergence problems encountered in a single NLS optimization over the entire estimation data set. Even if this did not present a logistical quagmire which it surely does this also requires a huge increase in the required computations a factor of approximately 1700 here . Some means of approximating the cross-validated MSE is thus required. Here we adopt the expedient of viewing the hidden unit coefficients obtained by the initial NLS on the estimation set as identifying potentially useful predictive transforms of the underlying variables and hold these fixed in cross-validation. Thus we only need to re-compute the hidden-to-output coefficients by OLS for each validation block. As mentioned above this can be done in a highly computationally efficient manner using Racine s 1997 feasible block cross-validation method. This might well result in overly optimistic cross-validated estimates of MSE but without some such approximation the exercise is not feasible. The exercise avoiding such approximations might be feasible on a supercomputer but as we see shortly this brute force NLS approach is dominated by QuickNet so the effort is not likely justified. Table 1 reports a subset of the results for this first exercise. Here we report two summary measures of goodness of