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A universal approach to estimate the conditional variance in semimartingale limit theorems

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  • Mathias Vetter

    (Christian-Albrechts-Universität zu Kiel)

Abstract

The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard task, in particular when the underlying process contains jumps. For this reason, several authors have recently discussed methods to automatically estimate the conditional variance, i.e. they build a consistent estimator from the original statistics, but computed at different time scales. Their methods work in several situations, but are essentially restricted to the case of continuous paths always. The aim of this work is to present a new method to consistently estimate the conditional variance which works regardless of whether the underlying process is continuous or has jumps. We will discuss the case of power variations in detail and give insight to the heuristics behind the approach.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:aistmt:v:73:y:2021:i:6:d:10.1007_s10463-020-00781-0
    DOI: 10.1007/s10463-020-00781-0
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    References listed on IDEAS

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    1. Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(2), pages 331-368, April.
    2. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    3. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    4. 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.
    5. Christensen, K. & Podolskij, M. & Thamrongrat, N. & Veliyev, B., 2017. "Inference from high-frequency data: A subsampling approach," Journal of Econometrics, Elsevier, vol. 197(2), pages 245-272.
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