A Bayesian approach for nonparametric regression in the presence of correlated errors

Bayesian bandwidth estimation in a nonparametric functional regression is investigated under the presence of correlated errors. As the correlation structure is unknown, we estimate it by assuming a parametric function for the correlation, then encounter it in a Bayesian estimation process. Under this approach, the kernel likelihood and posterior density of bandwidth parameters are derived. As the Bayes estimates cannot be obtained in a closed form, we use the well-known Markov chain Monte Carlo (MCMC) technique to compute the Bayes estimates under the squared errors loss function. Finally, simulations with application on real economic data are proposed to show the performance of the proposed Bayesian approach.