  In this paper we investigate the problem of designing experiments for series
estimators in nonparametric regression models with correlated observations. We
use projection based estimators to derive an explicit solution of the best
linear oracle estimator in the continuous time model for all Markovian-type
error processes. These solutions are then used to construct estimators, which
can be calculated from the available data along with their corresponding
optimal design points. Our results are illustrated by means of a simulation
study, which demonstrates that the new series estimator has a better
performance than the commonly used techniques based on the optimal linear
unbiased estimators. Moreover, we show that the performance of the estimators
proposed in this paper can be further improved by choosing the design points
appropriately.
