Local Polynomials vs Neural Networks: some empirical evidences

In the context of Local Polynomial estimators the global bandwidth parameter takes one of most important roles. There are several methods to get a consistent estimator for it. In particular, starting from the Mean Square Error of Local Polynomial estimators, the “plug-in†method is often used. So, we propose to estimate this global bandwidth parameter via a Neural Network approach for models of conditional mean functions in a proper nonlinear time series environment. Further the problem is to evaluate some functionals which depend on unknown quantities such as: the derivatives of the unknown conditional mean function, the conditional variance and the density function of the data generating process.