Nonparametric Regression with Serially Correlated Errors

Motivated by the problem of setting prediction intervals in time series analysis, this investigation is concerned with recovering a regression function <i>m(X_t)</i> on the basis of noisy observations taking at random design points <i>X_t</i>. 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 <i>m(x)(/i) is asymptotically normally distributed. Using this result, we construct confidence bands for </i>m(x)</i>. Simulations will be conducted to assess the performance of these bands in finite-sample situations