On the asymptotic variance in nonparametric regression with fractional time-series errors

Abstract

This paper focuses on deriving explicit formulae of the asymptotic variance in nonparametric regression with fractional time-series errors. Unified formulae are obtained for fixed design models with long-memory, short-memory and antipersistent errors. It is also found that in strongly antipersistent case the Uniform kernel is no longer the minimum variance one and that for a fourth-order kernel the constant in the asymptotic variance for long-memory errors may be clearly smaller than that for i.i.d. errors. The results are applied to improving an existing data-driven algorithm. Practical performance of the proposed algorithm is illustrated with simulated and real data examples.