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Quantile regression estimation for discretely observed SDE models with compound Poisson jumps

Author

Listed:
  • Noh, Jungsik
  • Lee, Seung Y.
  • Lee, Sangyeol

Abstract

This paper proposes a quantile regression estimator for the diffusion parameter in diffusion processes with compound Poisson jumps. The method is based on discretely sampled observations at high frequency. We verify its consistency and exhibit its robustness to jumps through a simulation study.

Suggested Citation

  • Noh, Jungsik & Lee, Seung Y. & Lee, Sangyeol, 2012. "Quantile regression estimation for discretely observed SDE models with compound Poisson jumps," Economics Letters, Elsevier, vol. 117(3), pages 734-738.
  • Handle: RePEc:eee:ecolet:v:117:y:2012:i:3:p:734-738
    DOI: 10.1016/j.econlet.2011.12.067
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    References listed on IDEAS

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    1. Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
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    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
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    6. Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.
    7. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    8. Jang, Jiwook, 2007. "Jump diffusion processes and their applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 62-70, July.
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    10. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, August.
    11. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    12. Yasutaka Shimizu & Nakahiro Yoshida, 2006. "Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 227-277, October.
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    More about this item

    Keywords

    Quantile regression estimator; Jump diffusion process; Compound Poisson jumps; Discretely observed sample; Consistency;

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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