A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density |
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Affiliation: | 1. Department of Finance, Economics and Management School, Wuhan University, Wuhan, China;2. Economics and Management School, Wuhan University, Wuhan, China;1. Economics, Business School, University of Western Australia, Perth, Australia;2. TEI Stereas Elladas, University of Applied Sciences, Economics and Management of Tourist and Culture Units, Amfissa, Nea Poli, Greece;3. Open University of Cyprus, Latsia, Cyprus |
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Abstract: | The unknown error density of a nonparametric regression model is approximated by a mixture of Gaussian densities with means being the individual error realizations and variance a constant parameter. Such a mixture density has the form of a kernel density estimator of error realizations. An approximate likelihood and posterior for bandwidth parameters in the kernel-form error density and the Nadaraya–Watson regression estimator are derived, and a sampling algorithm is developed. 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. The proposed approach is demonstrated through a nonparametric regression model of the Australian All Ordinaries daily return on the overnight FTSE and S&P 500 returns. With the estimated bandwidths, the one-day-ahead posterior predictive density of the All Ordinaries return is derived, 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. |
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Keywords: | Bayes factors Kernel-form error density Metropolis–Hastings algorithm Posterior predictive density State-price density Value-at-risk |
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