Nonparametric regression with weakly dependent data: the discrete and continuous regressor case

Data-driven methods of bandwidth selection are necessary for the sound application of kernel methods, with benefits including but not limited to automatic dimensionality reduction in the presence of irrelevant regressors [P. Hall, Q. Li, and J.S. Racine, ‘Nonparametric estimation of regression functions in the presence of irrelevant regressors, Rev. Econ. Statist. 89 (2007), pp. 784–789] and the ability to handle the mix of discrete and continuous data often encountered in applied settings without resorting to sample splitting [J.S. Racine and Q. Li, Nonparametric estimation of regression functions with both categorical and continuous data, J. Econometrics 119(1) (2004), pp. 99–130]. Many existing results have been developed under the presumption of independence, which may not hold when one deals with time-series data. This paper develops the properties of data-driven kernel regression for weakly dependent mixed discrete and continuous data. Monte Carlo simulations are undertaken to examine the finite-sample properties of the estimator, and an illustrative application is presented.