On conditional variance estimation in nonparametric regression

In this paper we consider a nonparametric regression model in which the conditional variance function is assumed to vary smoothly with the predictor. We offer an easily implemented and fully Bayesian approach that involves the Markov chain Monte Carlo sampling of standard distributions. This method is based on a technique utilized by Kim, Shephard, and Chib (in Rev. Econ. Stud. 65:361–393, 1998) for the stochastic volatility model. Although the (parametric or nonparametric) heteroscedastic regression and stochastic volatility models are quite different, they share the same structure as far as the estimation of the conditional variance function is concerned, a point that has been previously overlooked. Our method can be employed in the frequentist context and in Bayesian models more general than those considered in this paper. Illustrations of the method are provided.