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Handbook of Economic Forecasting part 10

Handbook of Economic Forecasting part 10. 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 | 64 J. Geweke and C. Whiteman Table 4 Comparison of forecast RMSE in Villani 2001 P specified empirical Bayes ECM 0.485 0.488 ML unrestricted ECM 0.773 0.694 ML restricted ECM 0.675 0.532 known coefficients ML unrestricted ECM and finds the forecast root mean square error. Finally it constrains many of the coefficients to zero using conventional stepwise deletion procedures in conjunction with maximum likelihood estimation and again finds the forecast root mean square error. Taking averages of these root mean square errors over forecasting horizons of one to eight quarters ahead yields comparison given in Table 4. The Bayesian ECM produces by far the lowest root mean square error of forecast and results are about the same whether the restricted or unrestricted version of the cointegrating vectors are used. The forecasts based on restricted maximum likelihood estimates benefit from the additional restrictions imposed by stepwise deletion of coefficients which is a crude from of shrinkage. In comparison with Shoesmith 1995 Villani 2001 has the further advantage of having used a full Monte Carlo simulation of the predictive density whose mean is the Bayes estimate given a squared-error loss function. These findings are supported by other studies that have made similar comparisons. An earlier literature on regional forecasting of which the seminal paper is Lesage 1990 contains results that are broadly consistent but not directly comparable because of the differences in variables and data. Amisano and Serati 1999 utilized a three-variable VAR for Italian GDP consumption and investment. Their approach was closer to mixed estimation than to full Bayesian inference. They employed not only a conventional Minnesota prior for the short-run dynamics but also applied a shrinkage prior to the factor loading vector a in 77 . This combination produced a smaller root mean square error for forecasts from one to twenty quarters ahead than either a traditional VAR with a Minnesota .