Semi-Parametric Single-Index Predictive Regression Models with Cointegrated Regressors

This paper considers the estimation of a semi-parametric single-index regression model that allows for nonlinear predictive relationships. This model is useful for predicting financial asset returns, whose observed behavior is described by a stationary process, when the multiple non-stationary predictors are co-integrated. The single-index specification, which uses the co-integrated predictors, not only balances the nonstationarity properties of the multiple predictors with the stationarity properties of asset returns but also avoids the curse of dimensionality associated with non-parametric regression function estimation. An orthogonal series expansion is used to approximate the unknown link function for the single-index component. We consider the constrained nonlinear least squares estimator of the single-index (or the co-integrating) parameters and the plug-in estimator of the link function, and derive their asymptotic properties. In an empirical application, we find some evidence of in-sample nonlinear predictability of U.S. stock returns using co-integrated predictors. We also find that the single-index model in general produces better out-of-sample forecasts than both the historical average benchmark and the linear predictive regression model