Unexpected opportunities in misspecified predictive regressions
研究发现，在模型错误设定下，即使因变量与自变量不相关，样本外R²也可能显著为正，为预测者带来意外收益；当变量高度持久时，相关性越低R²反而越高。
This article documents surprising learning patterns that can occur under model misspecification. An agent resorts to predictive regressions and fails to take into account autocorrelation in the dependent variable. Remarkably, when the dependent and independent variables are uncorrelated, we find cases for which the resulting out-of-sample R2 is well above zero, which benefits the agent, in spite of the erroneous model. We refer to them as instances of unexpected opportunity. When both variables exhibit high levels of persistence, we reveal the existence of counter-intuitive configurations for which the R2 increases when the absolute correlation between the series decreases. Our theoretical results are confirmed by extensive simulations and complemented by an empirical exercise of equity premium prediction for which we use 15 predictors commonly referenced in the economic literature.