Combining Many Forecasts with General Loss Functions

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Economic time series are often difficult to predict and as a result different forecasters, faced with predicting the same economic variable, often come up with very different answers, reflecting their use of separate forecasting models, information sets and estimation methods. It is very rare for any individual forecast to systematically dominate the others. Many studies have found that a simple equal-weighted combination of forecasts produces better predictions than those generated by individual models. This project develops both theoretical tools and empirical techniques for explaining why simple equal-weighted forecasts do so well in practice and compares these with wider classes of combinations. The research project develops estimation and forecast combination methods that can compete with the equal-weighted forecast combination. We establish conditions under which our proposed methods can be expected to produce improved forecast. The research project also considers the performance of different forecast combination methods under a host of economic circumstances, including prediction of economic variables in the near, medium and distant future, prediction of the entire probability distribution of an economic variable and prediction with loss functions that are tailored to individual policy makers or economic decision makers. The proposal also investigates the possibility of letting the forecast combination weights vary over time since some models may work better in some situations (e.g. when the economy is in a recession) and others may prove to be better in different circumstances (e.g. an expansion state). Forecast combination techniques have already been found to be useful in practical situations. This proposal provides further understanding of why this is so and explores various alternative approaches both theoretically and in practice, particularly when many forecasts are involved, and expands the approach in new ways. The interest in developing these methods is in part driven by practical concerns of the Principal Investigators that has come through interaction with the various Federal Reserve banks and other international organizations such as the IMF and through considering their needs and requests. We expect to continue strong relations with these and other organizations through the grant period.