  The problem of estimating the regression function in a fixed design models
with correlated observations is considered. Such observations are obtained from
several experimental units, each of them forms a time series. Based on the
trapezoidal rule, we propose a simple kernel estimator and we derive the
asymptotic expression of its integrated mean squared error IMSE and its
asymptotic normality. The problems of the optimal bandwidth and the optimal
design with respect to the asymptotic IMSE are also investigated. Finally, a
simulation study is conducted to study the performance of the new estimator and
to compare it with the classical estimator of Gasser and M\"uller in a finite
sample set. In addition, we study the robustness of the optimal design with
respect to the misspecification of the autocovariance function.
