Nonparametric methods: estimation, analysis and applications to business cycles.

Summary This thesis focuses on the study of the properties of the regression function by non-parametric methods for dependent processes and the application of these methods in business cycle analysis. Below we summarize the theoretical and empirical results obtained in this framework. The first theoretical result concerns the bias, variance, quatratic error and asymptotic normality of two non-parametric estimators: nearest neighbor and radial basis function. The other theoretical result was the extension of the envelopment tests in the case of dependent processes allowing to compare different parametric and non-parametric methods. The asymptotic normality of the statistics associated with these tests was established. The empirical work has been to propose these non-parametric methods in the forecasting of real economic activities from economic indicators and financial variables, to overcome some assumptions considered very strong in the parametric approach. The interest of non-parametric methods has been found in the forecasting of gross domestic product (GDP) in the Eurozone. The role of financial variables in the choice of models and in the selection of variables has been reviewed.