Combining Nonparametric and Optimal Linear Time Series Predictions

Abstract

We introduce a semiparametric procedure for more efficient prediction of a strictly stationary process admitting an ARMA representation. The procedure is based on the estimation of the ARMA representation, followed by a nonparametric regression where the ARMA residuals are used as explanatory variables. Compared to standard nonparametric regression methods, the number of explanatory variables can be reduced because our approach exploits the linear dependence of the process. We establish consistency and asymptotic normality results for our estimator. Numerical experiments show that significant gains can be achieved with our approach. All the supplemental materials used by this article are available online.