Bayesian Bandwidth Estimation in Nonparametric Time-Varying Coefficient Models

Abstract

Bandwidth plays an important role in determining the performance of nonparametric estimators, such as the local constant estimator. In this article, we propose a Bayesian approach to bandwidth estimation for local constant estimators of time-varying coefficients in time series models. We establish a large sample theory for the proposed bandwidth estimator and Bayesian estimators of the unknown parameters involved in the error density. A Monte Carlo simulation study shows that (i) the proposed Bayesian estimators for bandwidth and parameters in the error density have satisfactory finite sample performance; and (ii) our proposed Bayesian approach achieves better performance in estimating the bandwidths than the normal reference rule and cross-validation. Moreover, we apply our proposed Bayesian bandwidth estimation method 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 forms of the time-varying coefficients. Supplementary materials for this article are available online.

KEY WORDS:

• Bandwidth
• Local constant estimator
• Markov chain Monte Carlo

SUPPLEMENTARY MATERIALS

The supplementary materials give the detailed proofs of Theorem 1 and Theorem 2.

ACKNOWLEDGMENTS

The authors extend their sincere thanks to the co-editor, an associate editor, and three referees for their insightful comments that helped improve the article substantially. The authors thank participants to several seminars and conferences, at which earlier versions of this article were presented, for their constructive comments and suggestions. Thanks also go to Maxwell King for enlightening discussion. This research is supported under the Australian Research Council’s Discovery Projects Scheme (under Grant Numbers: DP1095838, DP1096374, and DP130104229).