This paper deals with the study of the estimation of the functional regression
operator when the explanatory variable takes its values in some abstract space of
functions. The main goal of this paper is to establish the exact rate of convergence
of the mean squared error of the functional version of the Nadaraya–Watson kernel
estimator when the errors come from a stationary process under long or short memory
and based on random functional data. Moreover, these theoretical results are checked
through some simulations with regular (smooth) and irregular curves and then with
real data.
Keywords Random functional data · Kernel estimator · Mean squared error
(MSE) · Short and long memory process · Asymptotic distribution · ARFIMA and

EB00000004361K

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• Regression models with correlated errors based on functional random design