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Effects of Jumps and Small Noise in High-Frequency Financial Econometrics

Author

Listed:
  • Naoto Kunitomo

    (Meiji University)

  • Daisuke Kurisu

    (University of Tokyo)

Abstract

Several new statistical procedures for high-frequency financial data analysis have been developed to estimate risk quantities and test the presence of jumps in the underlying continuous-time financial processes. Although the role of micro-market noise is important in high-frequency financial data, there are some basic questions on the effects of presence of noise and jump in the underlying stochastic processes. When there can be jumps and (micro-market) noise at the same time, it is not obvious whether the existing statistical methods are reliable for applications in actual data analysis. We investigate the misspecification effects of jumps and noise on some basic statistics and the testing procedures for jumps proposed by Ait-Sahalia and Jacod (Ann Stat 37–1:184–222 2009; 38–5:3093–3123 2010) as an illustration. We find that their first test (testing the presence of jumps as a null-hypothesis) is asymptotically robust in the small-noise asymptotic sense against possible misspecifications while their second test (testing no-jumps as a null-hypothesis) is quite sensitive to the presence of noise.

Suggested Citation

  • Naoto Kunitomo & Daisuke Kurisu, 2017. "Effects of Jumps and Small Noise in High-Frequency Financial Econometrics," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(1), pages 39-73, March.
    • Handle: RePEc:kap:apfinm:v:24:y:2017:i:1:d:10.1007_s10690-017-9223-4
    DOI: 10.1007/s10690-017-9223-4
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    References listed on IDEAS

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    1. Kunitomo, Naoto & Sato, Seisho, 2013. "Separating Information Maximum Likelihood estimation of the integrated volatility and covariance with micro-market noise," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 282-309.
    2. Takaki Hayashi & Nakahiro Yoshida, 2008. "Asymptotic normality of a covariance estimator for nonsynchronously observed diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 367-406, June.
    3. Aït-Sahalia, Yacine & Jacod, Jean & Li, Jia, 2012. "Testing for jumps in noisy high frequency data," Journal of Econometrics, Elsevier, vol. 168(2), pages 207-222.
    4. Markus Bibinger & Markus Reiß, 2014. "Spectral Estimation of Covolatility from Noisy Observations Using Local Weights," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 23-50, March.
    5. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    6. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    7. Yingying Li & Per A. Mykland, 2015. "Rounding Errors and Volatility Estimation," Journal of Financial Econometrics, Oxford University Press, vol. 13(2), pages 478-504.
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