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Testing and detecting jumps based on a discretely observed process

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  • Fan, Yingying
  • Fan, Jianqing

Abstract

We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test in Aït-Sahalia and Jacod (2009), our new test enjoys the same asymptotic properties but has smaller variance. These results are justified both theoretically and numerically. We also propose a new procedure to locate the jumps. The jump identification problem reduces to a multiple comparison problem. We employ the false discovery rate approach to control the probability of type I error. Numerical studies further demonstrate the power of our new method.

Suggested Citation

  • Fan, Yingying & Fan, Jianqing, 2011. "Testing and detecting jumps based on a discretely observed process," Journal of Econometrics, Elsevier, vol. 164(2), pages 331-344, October.
    • Handle: RePEc:eee:econom:v:164:y:2011:i:2:p:331-344
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    References listed on IDEAS

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    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Fan, Jianqing & Wang, Yazhen, 2007. "Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1349-1362, December.
    8. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    9. Ait-Sahalia, Yacine, 2004. "Disentangling diffusion from jumps," Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528, December.
    10. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    11. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    12. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
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    Cited by:

    1. Yu-Min Yen, 2013. "Testing Jumps via False Discovery Rate Control," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-15, April.
    2. El Ouadghiri, Imane & Uctum, Remzi, 2016. "Jumps in equilibrium prices and asymmetric news in foreign exchange markets," Economic Modelling, Elsevier, vol. 54(C), pages 218-234.
    3. Matúš Maciak & Sebastiano Vitali, 2024. "Using interpolated implied volatility for analysing exogenous market changes," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    4. Yu, Chao & Fang, Yue & Zhao, Xujie & Zhang, Bo, 2013. "Kernel filtering of spot volatility in presence of Lévy jumps and market microstructure noise," MPRA Paper 63293, University Library of Munich, Germany, revised 10 Mar 2014.
    5. Imane El Ouadghiri & Remzi Uctum, 2015. "Jumps in Equilibrium Prices and Asymmetric News in Foreign Exchange Markets," Working Papers hal-04141414, HAL.
    6. José E. Figueroa-López & Jeffrey Nisen, 2019. "Second-order properties of thresholded realized power variations of FJA additive processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 431-474, October.
    7. Zhao, X. & Hong, S. Y. & Linton, O. B., 2024. "Jumps Versus Bursts: Dissection and Origins via a New Endogenous Thresholding Approach," Cambridge Working Papers in Economics 2449, Faculty of Economics, University of Cambridge.
    8. 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.
    9. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    10. Yacine Aït-Sahalia & Jianqing Fan & Roger J. A. Laeven & Christina Dan Wang & Xiye Yang, 2017. "Estimation of the Continuous and Discontinuous Leverage Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1744-1758, October.
    11. Xin Zhang & Donggyu Kim & Yazhen Wang, 2016. "Jump Variation Estimation with Noisy High Frequency Financial Data via Wavelets," Econometrics, MDPI, vol. 4(3), pages 1-26, August.
    12. Guangying Liu & Meiyao Liu & Jinguan Lin, 2022. "Testing the volatility jumps based on the high frequency data," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 669-694, September.

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