We compare several representative sophisticated model averaging and variable selection techniques of forecasting stock returns. When estimated traditionally, our results confirm that the simple combination of individual predictors is superior. However, sophisticated models improve dramatically once we combine them with the historical average and take parameter instability into account. An equal weighted combination of the historical average with the standard multivariate predictive regression estimated using the average windows method, for example, achieves a statistically significant monthly out-of-sample of 1.10% and annual utility gains of 2.34%. We obtain similar gains for predicting future macroeconomic conditions.
