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Estimating the Spot Covariation of Asset Prices – Statistical Theory and Empirical Evidence

Author

Listed:
  • Markus Bibinger
  • Nikolaus Hautsch
  • Peter Malec
  • Markus Reiss

Abstract

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semimartingale 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

  • Markus Bibinger & Nikolaus Hautsch & Peter Malec & Markus Reiss, 2014. "Estimating the Spot Covariation of Asset Prices – Statistical Theory and Empirical Evidence," Cambridge Working Papers in Economics 1464, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1464
    Note: pm563
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    References listed on IDEAS

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    1. Federico M. Bandi & Roberto Reno, 2009. "Nonparametric Stochastic Volatility," Global COE Hi-Stat Discussion Paper Series gd08-035, Institute of Economic Research, Hitotsubashi University.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Markus Bibinger & Nikolaus Hautsch & Peter Malec & Markus Reiss, 2013. "Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency," SFB 649 Discussion Papers SFB649DP2013-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    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. 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.
    11. 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(03), pages 580-605, June.
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    Cited by:

    1. 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.
    2. Markus Bibinger & Lars Winkelmann, 2014. "Common price and volatility jumps in noisy high-frequency data," SFB 649 Discussion Papers SFB649DP2014-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. 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.

    More about this item

    Keywords

    local method of moments; spot covariance; smoothing; intraday (co-)variation risk;

    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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