IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2013-7.html
   My bibliography  Save this paper

Bayesian Bandwidth Selection in Nonparametric Time-Varying Coefficient Models

Author

Listed:
  • Tingting Cheng
  • Jiti Gao
  • Xibin Zhang

Abstract

Bandwidth plays an important role in determining the performance of local linear estimators. In this paper, we propose a Bayesian approach to bandwidth selection for local linear estimation of time–varying coefficient time series models, where the errors are assumed to follow the Gaussian kernel error density. A Markov chain Monte Carlo algorithm is presented to simultaneously estimate the bandwidths for local linear estimators in the regression function and the bandwidth for the Gaussian kernel error–density estimator. A Monte Carlo simulation study shows that: 1) our proposed Bayesian approach achieves better performance in estimating the bandwidths for local linear estimators than normal reference rule and cross–validation; 2) compared with the parametric assumption of either the Gaussian or the mixture of two Gaussians, Gaussian kernel error–density assumption is a data–driven choice and helps gain robustness in terms of different specification of the true error density. Moreover, we apply our proposed Bayesian sampling method to the estimation of bandwidth for the time–varying coefficient models that explain Okun’s law and the relationship between consumption growth and income growth in the U.S. For each model, we also provide calibrated parametric form of its time–varying coefficients.

Suggested Citation

  • Tingting Cheng & Jiti Gao & Xibin Zhang, 2013. "Bayesian Bandwidth Selection in Nonparametric Time-Varying Coefficient Models," Monash Econometrics and Business Statistics Working Papers 7/13, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2013-7
    as

    Download full text from publisher

    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp07-13.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Huyên Pham, 2000. "On quadratic hedging in continuous time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 315-339, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jan Kallsen & Richard Vierthauer, 2009. "Quadratic hedging in affine stochastic volatility models," Review of Derivatives Research, Springer, vol. 12(1), pages 3-27, April.
    2. Hepperger, Peter, 2012. "Hedging electricity swaptions using partial integro-differential equations," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 600-622.
    3. Cl'ement M'enass'e & Peter Tankov, 2015. "Asymptotic indifference pricing in exponential L\'evy models," Papers 1502.03359, arXiv.org, revised Feb 2015.
    4. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2022. "Sandwiched Volterra Volatility model: Markovian approximations and hedging," Papers 2209.13054, arXiv.org.
    5. Dong, Chaohua & Gao, Jiti, 2013. "Solving replication problems in a complete market by orthogonal series expansion," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 306-317.
    6. Anne Eyraud-Loisel, 2013. "Quadratic hedging in an incomplete market derived by an influent informed investor," Post-Print hal-00450949, HAL.
    7. Ariel Neufeld & Philipp Schmocker, 2022. "Chaotic Hedging with Iterated Integrals and Neural Networks," Papers 2209.10166, arXiv.org, revised Feb 2023.
    8. Koichi Matsumoto, 2009. "Dynamic programming and mean-variance hedging with partial execution risk," Review of Derivatives Research, Springer, vol. 12(1), pages 29-53, April.
    9. Alev{s} v{C}ern'y & Christoph Czichowsky, 2022. "The law of one price in quadratic hedging and mean-variance portfolio selection," Papers 2210.15613, arXiv.org, revised Jan 2024.
    10. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    11. Koichi Matsumoto, 2009. "Mean-Variance Hedging with Uncertain Trade Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 219-252.
    12. Junichi Imai, 2022. "A Numerical Method for Hedging Bermudan Options under Model Uncertainty," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 893-916, June.
    13. Chonghu Guan & Xiaomin Shi & Zuo Quan Xu, 2022. "Continuous-time Markowitz's mean-variance model under different borrowing and saving rates," Papers 2201.00914, arXiv.org, revised May 2023.
    14. Kamil Kladivko & Mihail Zervos, 2017. "Valuation of Employee Stock Options (ESOs) by means of Mean-Variance Hedging," Papers 1710.00897, arXiv.org.
    15. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," JRFM, MDPI, vol. 8(1), pages 1-20, February.
    16. Wan-Yi Chiu, 2021. "Mean-variance hedging in the presence of estimation risk," Review of Derivatives Research, Springer, vol. 24(3), pages 221-241, October.
    17. Okhrati, Ramin & Balbás, Alejandro & Garrido, José, 2014. "Hedging of defaultable claims in a structural model using a locally risk-minimizing approach," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2868-2891.
    18. Chonghu Guan & Xiaomin Shi & Zuo Quan Xu, 2023. "Continuous-Time Markowitz’s Mean-Variance Model Under Different Borrowing and Saving Rates," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 167-208, October.
    19. Vandaele, Nele & Vanmaele, Michèle, 2008. "A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1128-1137, June.
    20. Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833, arXiv.org, revised Jul 2017.

    More about this item

    Keywords

    Bayes factors; bandwidth; marginal likelihood; local linear estimator; random-walk Metropolis algorithm.;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2013-7. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.