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

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  • 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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    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.
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    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. Xiao, Zhijie & Koenker, Roger, 2009. "Conditional Quantile Estimation for Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1696-1712.
    8. Yacine Aït-Sahalia, 2001. "Transition Densities For Interest Rate And Other Nonlinear Diffusions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 1, pages 1-34, World Scientific Publishing Co. Pte. Ltd..
    9. 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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. Masuda, Hiroki, 2007. "Ergodicity and exponential [beta]-mixing bounds for multidimensional diffusions with jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(1), pages 35-56, January.
    12. 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.
    13. 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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    Cited by:

    1. Song, Yuping & Cai, Chunchun & Mao, Huijue & Zhu, Min, 2024. "Self-weighted quantile regression estimation for diffusion parameter in jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 206(C).

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    More about this item

    Keywords

    Quantile regression estimator; Jump diffusion process; Compound Poisson jumps; Discretely observed sample; Consistency;
    All these keywords.

    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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