Bayesian Bandwidth Selection in Nonparametric Time-Varying Coefficient Models

Abstract

Bandwidth plays an important role in determining the performance of local linear estimators. In this paper, we propose a Bayesian approach to bandwidth selection for local linear estimation of time-varying coefficient time series models, where the errors are assumed to follow the Gaussian kernel error density. A Markov chain Monte Carlo algorithm is presented to simultaneously estimate the bandwidths for local linear estimators in the regression function and the bandwidth for the Gaussian kernel error-density estimator. A Monte Carlo simulation study shows that: 1) our proposed Bayesian approach achieves better performance in estimating the bandwidths for local linear estimators than normal reference rule and cross-validation; 2) compared with the parametric assumption of either the Gaussian or the mixture of two Gaussians, Gaussian kernel error-density assumption is a data-driven choice and helps gain robustness in terms of different specification of the true error density. Moreover, we apply our proposed Bayesian sampling method to the estimation of bandwidth for the time-varying coefficient models that explain Okun's law and the relationship between consumption growth and income growth in the U.S. For each model, we also provide calibrated parametric form of its time-varying coefficients.