Advanced Search
MyIDEAS: Login to save this paper or follow this series

Bayesian estimation of bandwidths for a nonparametric regression model with a flexible error density

Contents:

Author Info

  • Xibin Zhang

    ()

  • Maxwell L. King

    ()

  • Han Lin Shang

    ()

Abstract

We approximate the 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. We investigate the construction of a likelihood and posterior for bandwidth parameters under this Gaussian-component mixture density of errors in a nonparametric regression. A Markov chain Monte Carlo algorithm is presented to sample bandwidths for the kernel estimators of the regression function and error density. A simulation study shows that the proposed Gaussian-component mixture density of errors is clearly favored against wrong assumptions of the error density. We apply our sampling algorithm to a nonparametric regression model of the All Ordinaries daily return on the overnight FTSE and S&P 500 returns, where the error density is approximated by the proposed mixture density. With the estimated bandwidths, we estimate the density of the one-step-ahead point forecast of the All Ordinaries return, and therefore, a distribution-free value-at-risk is obtained. The proposed Gaussian component mixture density of regression errors is also validated through the nonparametric regression involved in the state-price density estimation proposed by Aït-Sahalia and Lo (1998).

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp10-11.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 10/11.

as in new window
Length: 39 pages
Date of creation: 22 Aug 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-10

Contact details of provider:
Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Phone: +61-3-9905-2489
Fax: +61-3-9905-5474
Email:
Web page: http://www.buseco.monash.edu.au/depts/ebs/
More information through EDIRC

Order Information:
Email:
Web: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/

Related research

Keywords: Bayes factors; Gaussian-component mixture density; Markov chain Monte Carlo; state-price density; value-at-risk.;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. W. E. Griffiths, 1999. "Estimating consumer surplus comments on "using simulation methods for bayesian econometric models: inference development and communication"," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 75-87.
  2. Y. K. Tse & Xibin Zhang & Jun Yu, 2004. "Estimation of hyperbolic diffusion using the Markov chain Monte Carlo method," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 158-169.
  3. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  4. Linton, Oliver Bruce & Xiao, Zhijie, 2001. "A nonparametric regression estimator that adapts to error distribution of unknown form," SFB 373 Discussion Papers 2001,33, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  5. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  6. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
  7. G. M. Martin & C. S. Forbes, 1999. "Using simulation methods for bayesian econometric models: inference, development and communication: some comments," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 113-118.
  8. Y.K. Tse & Xibin Zhang & Jun Yu, 2002. "Estimation of Hyperbolic Diffusion Using MCMC Method," Monash Econometrics and Business Statistics Working Papers 18/02, Monash University, Department of Econometrics and Business Statistics.
  9. Huynh, Kim & Kervella, Pierre & Zheng, Jun, 2002. "Estimating state-price densities with nonparametric regression," SFB 373 Discussion Papers 2002,40, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  10. Ao Yuan & Jan G. De Gooijer, 2006. "Semiparametric Regression with Kernel Error Model," Tinbergen Institute Discussion Papers 06-058/4, Tinbergen Institute.
  11. Xibin Zhang & Maxwell L. King, 2011. "Bayesian semiparametric GARCH models," Monash Econometrics and Business Statistics Working Papers 24/11, Monash University, Department of Econometrics and Business Statistics.
  12. Zhang, Xibin & Brooks, Robert D. & King, Maxwell L., 2009. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Journal of Econometrics, Elsevier, vol. 153(1), pages 21-32, November.
  13. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
  2. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2013. "Bayesian bandwidth selection for a nonparametric regession model with mixed types of regressors," Monash Econometrics and Business Statistics Working Papers 13/13, Monash University, Department of Econometrics and Business Statistics.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2011-10. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Simone Grose).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.