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Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

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  • Per A. Mykland
  • Lan Zhang

Abstract

The availability of high frequency financial data has generated a series of estimators based on intra‐day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated. Standard errors are important: they are used to assess the precision of estimators in the form of confidence intervals, to create “feasible statistics” for testing, to build forecasting models based on, say, daily estimates, and also to optimize the tuning parameters. The contribution of this paper is to provide an alternative and general solution to this problem, which we call Observed Asymptotic Variance. It is a general nonparametric method for assessing asymptotic variance (AVAR). It provides consistent estimators of AVAR for a broad class of integrated parameters Θ = ∫ θ t dt, where the spot parameter process θ can be a general semimartingale, with continuous and jump components. The observed AVAR is implemented with the help of a two‐scales method. Its construction works well in the presence of microstructure noise, and when the observation times are irregular or asynchronous in the multivariate case. The methodology is valid for a wide variety of estimators, including the standard ones for variance and covariance, and also for more complex estimators, such as, of leverage effects, high frequency betas, and semivariance.

Suggested Citation

  • Per A. Mykland & Lan Zhang, 2017. "Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance," Econometrica, Econometric Society, vol. 85, pages 197-231, January.
  • Handle: RePEc:wly:emetrp:v:85:y:2017:i::p:197-231
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    Cited by:

    1. Torben G. Andersen & Martin Thyrsgaard & Viktor Todorov, 2019. "Cross-Sectional Dispersion of Risk in Trading Time," NBER Working Papers 26329, National Bureau of Economic Research, Inc.
    2. Yuan Liao & Xiye Yang, 2017. "Uniform Inference for Characteristic Effects of Large Continuous-Time Linear Models," Papers 1711.04392, arXiv.org, revised Dec 2018.
    3. Makoto Nakakita & Teruo Nakatsuma, 2021. "Bayesian Analysis of Intraday Stochastic Volatility Models of High-Frequency Stock Returns with Skew Heavy-Tailed Errors," JRFM, MDPI, vol. 14(4), pages 1-29, March.
    4. 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.
    5. Chen, Dachuan, 2024. "High frequency principal component analysis based on correlation matrix that is robust to jumps, microstructure noise and asynchronous observation times," Journal of Econometrics, Elsevier, vol. 240(1).
    6. Kim Christensen & Alexei Kolokolov, 2024. "An unbounded intensity model for point processes," Papers 2408.06519, arXiv.org.
    7. Mykland, Per A. & Zhang, Lan & Chen, Dachuan, 2019. "The algebra of two scales estimation, and the S-TSRV: High frequency estimation that is robust to sampling times," Journal of Econometrics, Elsevier, vol. 208(1), pages 101-119.
    8. Yuan Liao & Xiye Yang, 2017. "Uniform Inference for Conditional Factor Models with Instrumental and Idiosyncratic Betas," Departmental Working Papers 201711, Rutgers University, Department of Economics.
    9. Chen, Dachuan & Mykland, Per A. & Zhang, Lan, 2024. "Realized regression with asynchronous and noisy high frequency and high dimensional data," Journal of Econometrics, Elsevier, vol. 239(2).
    10. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility regressions with fat tails," Journal of Econometrics, Elsevier, vol. 218(2), pages 690-713.
    11. Mathias Vetter, 2021. "A universal approach to estimate the conditional variance in semimartingale limit theorems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1089-1125, December.
    12. Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.
    13. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility Regressions with Fat Tails," TSE Working Papers 20-1097, Toulouse School of Economics (TSE).
    14. Mykland, Per A. & Zhang, Lan, 2021. "The Observed Asymptotic Variance: Hard edges, and a regression approach," Journal of Econometrics, Elsevier, vol. 222(1), pages 411-428.
    15. Jihyun Kim & Nour Meddahi, 2020. "Volatility Regressions with Fat Tails," Post-Print hal-03142647, HAL.

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