Semi-parametric single-index predictive regression models with cointegrated regressors
提出一种半参数单指标回归模型，用于在多个非平稳预测变量协整时预测金融资产收益，通过单指标结构避免维数诅咒，并发现该模型对美国股票收益的样本内和样本外预测优于历史均值和线性模型。
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 behaviour resembles a stationary process, if the multiple nonstationary predictors are cointegrated. The presence of cointegrated regressors imposes a single-index structure in the model, and this structure 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 nonparametric 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 cointegrating) 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 cointegrated 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.