Nonparametric Regression with Serially Correlated Errors

Motivated by the problem of setting prediction intervals in time seriesanalysis, this investigation is concerned with recovering a regression functionm(X_t) on the basis of noisy observations taking at random design pointsX_t.It is presumed that the corresponding observations are corrupted by additiveserially correlated noise and that the noise is, in fact, induced by a generallinear process. The main result of this study is that, under some reasonableconditions, the nonparametric kernel estimator of m(x)(/i) is asymptoticallynormally distributed. Using this result, we construct confidence bands form(x).Simulations will be conducted to assess the performance of these bands infinite-sample situations