A nonparametric predictive regression model using partitioning estimators based on Taylor expansions

Abstract

This article proposes a nonparametric predictive regression model. The unknown function modeling the predictive relationship is approximated using polynomial Taylor expansions applied over disjoint intervals covering the support of the predictor variable. The model is estimated using the theory on partitioning estimators that is extended to a stationary time series setting. We show pointwise and uniform convergence of the proposed estimator and derive its asymptotic normality. These asymptotic results are applied to test for the presence of predictive ability. We develop an asymptotic pointwise test of predictive ability using the critical values of a Normal distribution, and a uniform test with asymptotic distribution that is approximated using a p-value transformation and Wild bootstrap methods. These theoretical insights are illustrated in an extensive simulation exercise and also in an empirical application to forecasting high-frequency based realized volatility measures. Our results provide empirical support to the presence of nonlinear autoregressive predictability of these measures for the constituents of the Dow Jones index.