Nonparametric regression with serially correlated errors

Motivated by the problem of setting prediction intervals in time series analysis, this investigation is concerned with recovering regression function m(X_t) on the basis of noisy observations taking at random design points X_t. It is presumed that the corresponding observations are corrupted by additive serially correlated noise and that the noise is, in fact, induced by a general linear process. The main result of this study is that, under some reasonable conditions, the nonparametric kernel estimator of m(x) is asymptotically normally distributed. The result can be used to construct confidence bands for m(x). Simulations are conducted to assess the performance of these bands in finite-sample situations.