To Combine Forecasts or to Combine Information?

When the objective is to forecast a variable of interest but with many explanatory variables available, one could possibly improve the forecast by carefully integrating them. There are generally two directions one could proceed: combination of forecasts (CF) or combination of information (CI). CF combines forecasts generated from simple models each incorporating a part of the whole information set, while CI brings the entire information set into one super model to generate an ultimate forecast. Through linear regression analysis and simulation, we show the relative merits of each, particularly the circumstances where forecast by CF can be superior to forecast by CI, when CI model is correctly specified and when it is misspecified, and shed some light on the success of equally weighted CF. In our empirical application on prediction of monthly, quarterly, and annual equity premium, we compare the CF forecasts (with various weighting schemes) to CI forecasts (with principal component approach mitigating the problem of parameter proliferation). We find that CF with (close to) equal weights is generally the best and dominates all CI schemes, while also performing substantially better than the historical mean.

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