Hermite Series Estimation in Nonlinear Cointegrating Models

This paper discusses nonparametric series estimation of integrable cointegration models using Hermite functions. We establish the uniform consistency and asymptotic normality of the series estimator. The Monte Carlo simulation results show that the performance of the estimator is numerically satisfactory. We then apply the estimator to estimate the stock return predictive function. The out-of-sample evaluation results suggest that dividend yield has nonlinear predictive power for stock returns while book-to-market ratio and earning-price ratio have little predictive power.