TD n. 604 2012

Eric Hillebrand, Tae-Hwy Lee , Marcelo Medeiros.

The literature on excess return prediction has considered a wide array of estimation schemes, among them unrestricted and restricted regression coefficients. We consider bootstrap aggregation (bagging) to smooth parameter restrictions. Two types of restrictions are considered: positivity of the regression coefficient and positivity of the forecast. Bagging constrained estimators can have smaller asymptotic mean-squared prediction errors than forecasts from a restricted model without bagging. Monte Carlo simulations show that forecast gains can be achieved in realistic sample sizes for the stock return problem. In an empirical application using the data set of Campbell, J., and S. Thompson (2008): “Predicting the Equity Premium Out of Sample: Can Anything Beat the Historical Average?”, Review of Financial  tudies 21, 1511-1531, we show that we can improve the forecast performance further by smoothing the restriction through bagging.