A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation

Xibin Zhang (), Robert D. Brooks () and Maxwell King

No 11/07, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Multivariate kernel regression is an important tool for investigating the relationship between a response and a set of explanatory variables. It is generally accepted that the performance of a kernel regression estimator largely depends on the choice of bandwidth rather than the kernel function. This nonparametric technique has been employed in a number of empirical studies including the state-price density estimation pioneered by Aït-Sahalia and Lo (1998). However, the widespread usefulness of multivariate kernel regression has been limited by the difficulty in computing a data-driven bandwidth. In this paper, we present a Bayesian approach to bandwidth selection for multivariate kernel regression. A Markov chain Monte Carlo algorithm is presented to sample the bandwidth vector and other parameters in a multivariate kernel regression model. A Monte Carlo study shows that the proposed bandwidth selector is more accurate than the rule-of-thumb bandwidth selector known as the normal reference rule according to Scott (1992) and Bowman and Azzalini (1997). The proposed bandwidth selection algorithm is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow-Debreu securities. When applying the proposed method to the S&P 500 index options and the DAX index options, we find that for short-maturity options, the proposed Bayesian bandwidth selector produces an obviously different state-price density from the one produced by using a subjective bandwidth selector discussed in Aït-Sahalia and Lo (1998).

Keywords: Black-Scholes formula; Likelihood; Markov chain Monte Carlo; Posterior density. (search for similar items in EconPapers)
JEL-codes: C11 C14 G12 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2007-08
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (5)

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Related works:
Journal Article: A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation (2009)
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