We develop a framework for estimating expected returns---a <i>predictive system</i>---that allows predictors to be imperfectly correlated with the conditional expected return. When predictors are imperfect, the estimated expected return depends on past returns in a manner that hinges on the correlation...

The standard regression approach to modeling return predictability seems too restrictive in one way but too lax in another. A predictive regression models expected returns as an exact linear function of a given set of predictors but does not exploit the likely economic property that innovations...