  A linear multiple regression model in function spaces is formulated, under
temporal correlated errors. This formulation involves kernel regressors. A
generalized least-squared regression parameter estimator is derived. Its
asymptotic normality and strong consistency is obtained, under suitable
conditions. The correlation analysis is based on a componentwise estimator of
the residual autocorrelation operator. When the dependence structure of the
functional error term is unknown, a plug-in generalized least-squared
regression parameter estimator is formulated. Its strong-consistency is proved
as well. A simulation study is undertaken to illustrate the performance of the
presented approach, under different regularity conditions. An application to
financial panel data is also considered.
