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The Observed Asymptotic Variance: Hard edges, and a regression approach

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  • Mykland, Per A.
  • Zhang, Lan

Abstract

High frequency financial data has become an essential component of the digital economy, yielding an increasing number of estimators. However, it is hard to reliably assess the uncertainty of such estimators. The Observed Asymptotic Variance (observed AVAR) is a non-parametric estimator for (squared) standard error in high frequency data. The device is related to observed information in likelihood theory, but in this case it is non-parametric and uses the high-frequency data structure. An earlier paper has developed the estimator in the case where edge effects are small to moderate. In practical data, it is often more realistic to assume that edge effects can be large, and this is the problem that we tackle in the current paper. We here find a regression approach to observed AVAR which is highly robust to large edges. This approach covers most high frequency estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:222:y:2021:i:1:p:411-428
    DOI: 10.1016/j.jeconom.2020.07.008
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    References listed on IDEAS

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    1. Mykland, Per A. & Zhang, Lan, 2016. "Between data cleaning and inference: Pre-averaging and robust estimators of the efficient price," Journal of Econometrics, Elsevier, vol. 194(2), pages 242-262.
    2. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2012. "Jump-robust volatility estimation using nearest neighbor truncation," Journal of Econometrics, Elsevier, vol. 169(1), pages 75-93.
    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. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2014. "A Robust Neighborhood Truncation Approach To Estimation Of Integrated Quarticity," Econometric Theory, Cambridge University Press, vol. 30(1), pages 3-59, February.
    5. Markus Bibinger & Per A. Mykland, 2016. "Inference for Multi-dimensional High-frequency Data with an Application to Conditional Independence Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1078-1102, December.
    6. 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.
    7. Dachuan Chen & Per A. Mykland & Lan Zhang, 2020. "The Five Trolls Under the Bridge: Principal Component Analysis With Asynchronous and Noisy High Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1960-1977, December.
    8. 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.
    9. 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.
    10. Aït-Sahalia, Yacine & Xiu, Dacheng, 2019. "A Hausman test for the presence of market microstructure noise in high frequency data," Journal of Econometrics, Elsevier, vol. 211(1), pages 176-205.
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