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Estimating the spot covariation of asset prices: Statistical theory and empirical evidence

Author

Listed:
  • Bibinger, Markus
  • Hautsch, Nikolaus
  • Malec, Peter
  • Reiss, Markus
Abstract
We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced by Bibinger et al. (2014). We extend the LMM estimator to allow for autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. We prove the consistency and asymptotic normality of the proposed spot covariance estimator. Based on extensive simulations we provide empirical guidance on the optimal implementation of the estimator and apply it to high-frequency data of a cross-section of NASDAQ blue chip stocks. Employing the estimator to estimate spot covariances, correlations and betas in normal but also extreme-event periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, (iii) are strongly serially correlated, and (iv) can increase strongly and nearly instantaneously if new information arrives.

Suggested Citation

  • Bibinger, Markus & Hautsch, Nikolaus & Malec, Peter & Reiss, Markus, 2014. "Estimating the spot covariation of asset prices: Statistical theory and empirical evidence," CFS Working Paper Series 477, Center for Financial Studies (CFS).
    • Handle: RePEc:zbw:cfswop:477
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    References listed on IDEAS

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    1. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    2. Hayashi, Takaki & Yoshida, Nakahiro, 2011. "Nonsynchronous covariation process and limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2416-2454, October.
    3. 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.
    4. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 456-499.
    5. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    6. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2009. "Duration-Based Volatility Estimation," Global COE Hi-Stat Discussion Paper Series gd08-034, Institute of Economic Research, Hitotsubashi University.
    7. Nikolaus Hautsch & Mark 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, Taylor & Francis Journals, vol. 31(2), pages 165-183, April.
    8. Li, Yingying & Mykland, Per A. & Renault, Eric & Zhang, Lan & Zheng, Xinghua, 2014. "Realized Volatility When Sampling Times Are Possibly Endogenous," Econometric Theory, Cambridge University Press, vol. 30(3), pages 580-605, June.
    9. Christensen, Kim & Podolskij, Mark & Vetter, Mathias, 2013. "On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 59-84.
    10. Charles S. Bos & Paweł Janus & Siem Jan Koopman, 2012. "Spot Variance Path Estimation and Its Application to High-Frequency Jump Testing," Journal of Financial Econometrics, Oxford University Press, vol. 10(2), pages 354-389, 2012 06.
    11. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    12. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    13. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    14. Kalnina, Ilze & Linton, Oliver, 2008. "Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error," Journal of Econometrics, Elsevier, vol. 147(1), pages 47-59, November.
    15. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-174, January.
    16. Peter Hansen & Jeremy Large & Asger Lunde, 2008. "Moving Average-Based Estimators of Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 79-111.
    17. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    18. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
    19. Bibinger, Markus & Winkelmann, Lars, 2013. "Econometrics of co-jumps in high-frequency data with noise," SFB 649 Discussion Papers 2013-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    20. De Santis, Giorgio & Gerard, Bruno, 1997. "International Asset Pricing and Portfolio Diversification with Time-Varying Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1881-1912, December.
    21. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
    22. Altmeyer, Randolf & Bibinger, Markus, 2014. "Functional stable limit theorems for efficient spectral covolatility estimators," SFB 649 Discussion Papers 2014-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    23. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    24. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    25. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    26. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    27. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    28. Bibinger, Markus & Hautsch, Nikolaus & Malec, Peter & Reiss, Markus, 2013. "Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency," SFB 649 Discussion Papers 2013-017, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    29. Zu, Yang & Peter Boswijk, H., 2014. "Estimating spot volatility with high-frequency financial data," Journal of Econometrics, Elsevier, vol. 181(2), pages 117-135.
    30. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(1), pages 60-93, February.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

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    3. Torben G. Andersen & Martin Thyrsgaard & Viktor Todorov, 2021. "Recalcitrant betas: Intraday variation in the cross‐sectional dispersion of systematic risk," Quantitative Economics, Econometric Society, vol. 12(2), pages 647-682, May.
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    5. Bibinger, Markus & Winkelmann, Lars, 2014. "Common price and volatility jumps in noisy high-frequency data," SFB 649 Discussion Papers 2014-037, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
    7. Hautsch, Nikolaus & Horvath, Akos, 2019. "How effective are trading pauses?," Journal of Financial Economics, Elsevier, vol. 131(2), pages 378-403.
    8. Tobias Eckernkemper & Bastian Gribisch, 2021. "Intraday conditional value at risk: A periodic mixed‐frequency generalized autoregressive score approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(5), pages 883-910, August.
    9. Chae-Deug, Yi, 2024. "Realized normal volatility and maximum outlying jumps in high frequency returns for Korean won–US Dollar," International Review of Financial Analysis, Elsevier, vol. 95(PA).
    10. Kim Christensen & Ulrich Hounyo & Zhi Liu, 2024. "A nonparametric test for diurnal variation in spot correlation processes," Papers 2408.02757, arXiv.org.
    11. Markus Bibinger & Nikolaus Hautsch & Alexander Ristig, 2024. "Jump detection in high-frequency order prices," Papers 2403.00819, arXiv.org.
    12. Bibinger, Markus & Neely, Christopher & Winkelmann, Lars, 2019. "Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 158-184.
    13. Jakob Albers & Mihai Cucuringu & Sam Howison & Alexander Y. Shestopaloff, 2021. "Fragmentation, Price Formation, and Cross-Impact in Bitcoin Markets," Papers 2108.09750, arXiv.org.
    14. Mustafayeva, Konul & Wang, Weining, 2020. "Non-Parametric Estimation of Spot Covariance Matrix with High-Frequency Data," IRTG 1792 Discussion Papers 2020-025, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    15. Žikica Lukić & Bojana Milošević, 2024. "A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 797-820, October.
    16. Bibinger, Markus & Madensoy, Mehmet, 2019. "Change-point inference on volatility in noisy Itô semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 4878-4925.
    17. Jacod, Jean & Mykland, Per A., 2015. "Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2910-2936.
    18. Rui Da & Dacheng Xiu, 2021. "When Moving‐Average Models Meet High‐Frequency Data: Uniform Inference on Volatility," Econometrica, Econometric Society, vol. 89(6), pages 2787-2825, November.
    19. Zhang, Congshan & Li, Jia & Bollerslev, Tim, 2022. "Occupation density estimation for noisy high-frequency data," Journal of Econometrics, Elsevier, vol. 227(1), pages 189-211.
    20. Giuseppe Buccheri & Giacomo Bormetti & Fulvio Corsi & Fabrizio Lillo, 2018. "A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: an Application to High-Frequency Covariance Dynamics," Papers 1803.04894, arXiv.org, revised Mar 2019.
    21. Dalderop, Jeroen, 2020. "Nonparametric filtering of conditional state-price densities," Journal of Econometrics, Elsevier, vol. 214(2), pages 295-325.
    22. Richard Y. Chen, 2019. "The Fourier Transform Method for Volatility Functional Inference by Asynchronous Observations," Papers 1911.02205, arXiv.org.
    23. Jir^o Akahori & Nien-Lin Liu & Maria Elvira Mancino & Tommaso Mariotti & Yukie Yasuda, 2023. "Symmetric positive semi-definite Fourier estimator of instantaneous variance-covariance matrix," Papers 2304.04372, arXiv.org.

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    More about this item

    Keywords

    local method of moments; spot covariance; smoothing; intraday (co-)variation risk;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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