Functional prediction of intraday cumulative returns

Abstract

We define cumulative intraday returns and consider their prediction from such returns on a market index. We model these returns as curves in a function space. We propose several functional regression models which can be viewed as extensions of the capital asset pricing model to intraday returns defined as curves. After deriving parameter estimates and prediction functions for these models, we compare their prediction errors by application to cumulative intraday returns of large U.S. corporations. We find that complex functional regression models do not perform better than a simple model. In particular, we find that modelling error dependence does not improve forecasts.