Electronic Journal of Statistics

Common price and volatility jumps in noisy high-frequency data

Markus Bibinger and Lars Winkelmann

Full-text: Open access


We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process. The proposed test is based on high-frequency data and is robust to market microstructure frictions. For the test, local estimators of volatility jumps at price jump arrival times are designed using a nonparametric spectral estimator of the spot volatility process. A simulation study and an empirical example with NASDAQ order book data demonstrate the practicability of the proposed methods and highlight the important role played by price volatility co-jumps.

Article information

Electron. J. Statist., Volume 12, Number 1 (2018), 2018-2073.

Received: June 2017
First available in Project Euclid: 18 June 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

High-frequency data microstructure noise nonparametric volatility estimation volatility jumps

Creative Commons Attribution 4.0 International License.


Bibinger, Markus; Winkelmann, Lars. Common price and volatility jumps in noisy high-frequency data. Electron. J. Statist. 12 (2018), no. 1, 2018--2073. doi:10.1214/18-EJS1444. https://projecteuclid.org/euclid.ejs/1529308886

Export citation


  • [1] Aït-Sahalia, Y., J. Fan, R. J. A. Laeven, C. D. Wang, and X. Yang (2017). Estimation of the continuous and discontinuous leverage effects., Journal of the American Statistical Association, 112(520), 1744–1758.
  • [2] Aït-Sahalia, Y. and J. Jacod (2010). Is Brownian motion necessary to model high-frequency data?, The Annals of Statistics 38(5), 3093–3128.
  • [3] Aït-Sahalia, Y. and J. Jacod (2014)., High-frequency financial econometrics. Princeton, NJ: Princeton University Press.
  • [4] Aït-Sahalia, Y., L. Zhang, and P. A. Mykland (2005). How often to sample a continuous-time process in the presence of market microstructure noise., Review of Financial Studies 18, 351–416.
  • [5] Altmeyer, R. and M. Bibinger (2015). Functional stable limit theorems for quasi-efficient spectral covolatility estimators., Stochastic Processes and their Applications 125(12), 4556–4600.
  • [6] Andersen, T. G. and T. Bollerslev (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts., International Economic Review 39(4), 885–905.
  • [7] Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys (2001). The distribution of realized exchange rate volatility., Journal of the American Statistical Association 96(453), 42–55.
  • [8] Bandi, F. and R. Renò (2016). Price and volatility co-jumps., Journal of Financial Economics 119(1), 107–146.
  • [9] Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard (2008). Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise., Econometrica 76(6), 1481–1536.
  • [10] Barndorff-Nielsen, O. E. and N. Shephard (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models., Journal of the Royal Statistical Society 64(2), 253–280.
  • [11] Bibinger, M. (2011). Efficient covariance estimation for asynchronous noisy high-frequency data., Scandinavian Journal of Statistics 38, 23–45.
  • [12] Bibinger, M., N. Hautsch, P. Malec, and M. Reiß (2014). Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency., The Annals of Statistics 42(4), 1312–1346.
  • [13] Bibinger, M., N. Hautsch, P. Malec, and M. Reiß (2017). Estimating the spot covariation of asset prices – statistical theory and empirical evidence., Journal of Business & Economic Statistics, forthcoming.
  • [14] Bibinger, M., M. Jirak, and M. Vetter (2017). Nonparametric change-point analysis of volatility., The Annals of Statistics 45(4), 1542–1578.
  • [15] Bibinger, M. and M. Reiß (2014). Spectral estimation of covolatility from noisy observations using local weights., Scandinavian Journal of Statistics 41(1), 23–50.
  • [16] Bibinger, M. and L. Winkelmann (2015). Econometrics of co-jumps in high-frequency data with noise., Journal of Econometrics 184(2), 361 – 378.
  • [17] Bloom, N. (2009). The impact of uncertainty shocks., Econometrica 77(3), 623–685.
  • [18] Clinet, S. and Y. Potiron (2017). Efficient asymptotic variance reduction when estimating volatility in high frequency data., arxive:1701.01185.
  • [19] Comte, F. and E. Renault (1998). Long memory in continuous-time stochastic volatility models., Mathematical Finance 8(4), 291–323.
  • [20] Duffie, D., J. Pan, and K. Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions., Econometrica 68(6), 1343–1376.
  • [21] Fan, J. and Y. Wang (2007). Multi-scale jump and volatility analysis for high-frequency data., Journal of the American Statistical Association 102(480), 1349–1362.
  • [22] Hansen, P. R. and A. Lunde (2006). Realized variance and market microstructure noise., Journal of Business & Economic Statistics 24(2), 127–161.
  • [23] Hautsch, N. and M. Podolskij (2013). Preaveraging-based estimation of quadratic variation in the presence of noise and jumps: Theory, implementation, and empirical evidence., Journal of Business & Economic Statistics 31(2), 165–183.
  • [24] Jacod, J. (2008). Asymptotic properties of realized power variations and related functionals of semimartingales., Stochastic Processes and their Applications 118(4), 517–559.
  • [25] Jacod, J., C. Klüppelberg, and G. Müller (2017). Testing for non-correlation between price and volatility jumps., Journal of Econometrics 197(2), 284–297.
  • [26] Jacod, J., Y. Li, P. A. Mykland, M. Podolskij, and M. Vetter (2009). Microstructure noise in the continous case: the pre-averaging approach., Stochastic Processes and their Applications 119, 2803–2831.
  • [27] Jacod, J. and P. A. Mykland (2015). Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method., Stochastic Processes and their Applications 125, 2910 – 2936.
  • [28] Jacod, J. and P. Protter (2012)., Discretization of processes. Springer.
  • [29] Jacod, J. and V. Todorov (2010). Do price and volatility jump together?, The Annals of Applied Probability 20(4), 1425–1469.
  • [30] Kalnina, I. and D. Xiu (2017). Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency., Journal of the American Statistical Association 112(517), 384–396.
  • [31] Koike, Y. (2016). Estimation of integrated covariances in the simultaneous presence of nonsynchronicity, microstructure noise and jumps., Econometric Theory 32(3), 533–611.
  • [32] Lee, S. and P. A. Mykland (2008). Jumps in finacial markets: A new nonparametric test and jump dynamics., Review of Financial Studies 21(6), 2535–2563.
  • [33] Lee, S. and P. A. Mykland (2012). Jumps in equilibrium prices and market microstructure noise., Journal of Econometrics 168(2), 396–406.
  • [34] Liu, J., F. Longstaff, and J. Pan (2003). Dynamic asset allocation with event risk., Journal of Finance 58(1), 231–259.
  • [35] Mancini, C. (2009). Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps., Scandinavian Journal of Statistics 36(4), 270–296.
  • [36] Mancini, C., V. Mattiussi, and R. Reno (2015). Spot volatility estimation using delta sequences., Finance and Stochastics 19(2), 261–293.
  • [37] Munk, A. and J. Schmidt-Hieber (2010a). Lower bounds for volatility estimation in microstructure noise models. In J. O. Berger, T. T. Cai, and I. M. Johnstone (Eds.), Borrowing Strength: Theory Powering Applications – A Festschrift for Lawrence D. Brown, Volume 6 of Collections, pp. 43–55. Beachwood, Ohio, USA: Institute of Mathematical Statistics.
  • [38] Munk, A. and J. Schmidt-Hieber (2010b). Nonparametric estimation of the volatility function in a high-frequency model corrupted by noise., Electronic Journal of Statistics 4, 781–821.
  • [39] Pastor, L. and P. Veronesi (2012). Uncertainty about government policy and stock prices., Journal of Finance 67(4), 1219–1264.
  • [40] Reiß, M. (2011). Asymptotic equivalence for inference on the volatility from noisy observations., The Annals of Statistics 39(2), 772–802.
  • [41] Tauchen, G. and V. Todorov (2011). Volatility jumps., Journal of Business and Economic Statistics 29(3), 356–371.
  • [42] Todorov, V. (2010). Variance risk-premium dynamics: The role of jumps., Review of Financial Studies 23(1), 345–383.
  • [43] Winkelmann, L., M. Bibinger, and T. Linzert (2016). Ecb monetary policy surprises: Identification through cojumps in interest rates., Journal of Applied Econometrics 31(4), 613–629.
  • [44] Zhang, L. (2006). Efficient estimation of stochastic volatility using noisy observations: A multi-scale approach., Bernoulli 12(6), 1019–1043.
  • [45] Zu, Y. and H. P. Boswijk (2014). Estimating spot volatility with high-frequency financial data., Journal of Econometrics 181(2), 117 – 135.