Choosing Among Competing Econometric Forecasts: Regression Based Forecast Combination Using Model Selection

Based on Monte Carlo simulations using both stationary and nonstationary data, a model selection approach which uses the SIC to select a "best" group of forecasts in the context of forecast combination regressions dominates a number of other techniques, including the standard t-statistic approach and the simple averaging rule. Our results are robust across various restricted and unrestricted versions of standard linear forecast combination specifications, and are not affected by the use of differenced or levels data. In addition to the Monte Carlo experiments, we conduct a real-time forecasting experiment using sequences of forecasts of nine macroeconomic variables. The forecasting models which we examine include linear VAR models, nonlinear artificial neural network models, and the Survey of Professional Forecasters (SPF). Based on ex ante performance, our empirical evidence suggests that the SIC dominates the other forecast combination strategies which are examined. Furthermore, when the SIC approach is used in the context of forecast encompassing type regressions, we conclude that "individual" forecasts are often preferred to combined weight forecasts, and that the SPF model and the econometric models each win approximately the same number of times. We also illustrate that collinearity among competing forecasts arises, even when only three competing forecasts are used in a linear forecast combination regression, and suggest that this is one of the reasons why information criteria are useful for constructing combined weight forecasts. This point is illustrated as tstatistics used to test the significance of alternative forecasts of simulated as well as actual data are often below a 10% critical value, suggesting that either none, or all competing forecasts should be used to construct combined weight forecasts, for example.