A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density

Xibin Zhang (), Maxwell King and Han Lin Shang

No 20/13, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: We propose to approximate the unknown error density of a nonparametric regression model by a mixture of Gaussian densities with means being the individual error realizations and variance a constant parameter. This mixture density has the form of a kernel density estimator of error realizations. We derive an approximate likelihood and posterior for bandwidth parameters in the kernel-form error density and the Nadaraya-Watson regression estimator and develop a sampling algorithm. A simulation study shows that when the true error density is non-Gaussian, the kernel-form error density is often favored against its parametric counterparts including the correct error density assumption. Our approach is demonstrated through a nonparametric regression model of the Australian All Ordinaries daily return on the overnight FTSE and S&P 500 returns. Using the estimated bandwidths, we derive the one-day-ahead density forecast of the All Ordinaries return, and a distribution-free value-at-risk is obtained. The proposed algorithm is also applied to a nonparametric regression model involved in state–price density estimation based on S&P 500 options data.

Keywords: Bayes factors; kernel-form error density; Metropolis-Hastings algorithm; state–price density; value-at-risk (search for similar items in EconPapers)
Date: 2013
New Economics Papers: this item is included in nep-ecm and nep-for
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Journal Article: A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density (2014)
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