The scale of predictability

Stock return predictive relations found to be elusive when using raw data may hold true for different layers in the cascade of economic shocks. Consistent with this logic, we model stock market returns and their predictors as aggregates of uncorrelated components (details) operating over different scales and introduce a notion of scale-specific predictability, i.e., predictability on the details. We study and formalize the link between scale-specific predictability and aggregation. Using both direct extraction of the details and aggregation, we provide strong evidence of risk compensations in long-run stock market returns - as well as of an unusually clear link between macroeconomic uncertainty and uncertainty in financial markets - at frequencies lower than the business cycle. The reported tent-shaped behavior in long-run predictability is shown to be a theoretical implication of our proposed modelling approach.