Predictive Systems: Living with Imperfect Predictors

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 in expected returns are negatively correlated with unexpected returns. We develop an alternative framework---a predictive system---that accommodates imperfect predictors and beliefs about that negative correlation. In this framework, the predictive ability of imperfect predictors is supplemented by information in lagged returns as well as lags of the predictors. Compared to predictive regressions, predictive systems deliver different and substantially more precise estimates of expected returns as well as different assessments of a given predictor's usefulness.