Nonparametric and Semiparametric Regressions Subject to Monotonicity Constraints: Estimation and Forecasting∗

This paper considers nonparametric and semiparametric regression models subject to monotonicity constraint. We use bagging as an alternative approach to Hall and Huang (2001). Asymptotic properties of our proposed estimators and forecasts are established. Monte Carlo simulation is conducted to show their finite sample performance. An application to predicting equity premium is taken for illustration. We introduce a new forecasting evaluation criterion based on the second order stochastic dominance in the size of forecast errors and compare models over different sizes of forecast errors. Imposing monotonicity constraint can mitigate the chance of making large size forecast errors.