Motivated by the problem of setting prediction intervals in time series analysis, this investigation is concerned with recovering a 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)(/i) is asymptotically normally distributed. Using this result, we construct confidence bands for m(x). Simulations will be conducted to assess the performance of these bands in finite-sample situations
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