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Efficient Estimation Of Integrated Volatility And Related Processes

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  • Renault, Eric
  • Sarisoy, Cisil
  • Werker, Bas J.M.

Abstract

We derive nonparametric efficiency bounds for regular estimators of integrated smooth transformations of instantaneous variances, in particular, integrated power variance. We find that realized variance attains the efficiency bound for integrated variance under both regular and irregular sampling schemes. For estimating higher powers such as integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds, when observation times are equidistant. Moreover, the estimator in Jacod and Rosenbaum (2013), whose efficiency was documented for the submodel assuming constant volatility, is efficient also for nonconstant volatility paths. When the observation times are possibly random but predictable, we provide an estimator, similar to that of Kristensen (2010), which can get arbitrarily close to the nonparametric bound. Finally, parametric information about the functional form of volatility leads to a lower efficiency bound, unless the volatility process is piecewise constant.

Suggested Citation

  • Renault, Eric & Sarisoy, Cisil & Werker, Bas J.M., 2017. "Efficient Estimation Of Integrated Volatility And Related Processes," Econometric Theory, Cambridge University Press, vol. 33(2), pages 439-478, April.
    • Handle: RePEc:cup:etheor:v:33:y:2017:i:02:p:439-478_00
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    Cited by:

    1. Jia Li & Dacheng Xiu, 2016. "Generalized Method of Integrated Moments for High‐Frequency Data," Econometrica, Econometric Society, vol. 84(4), pages 1613-1633, July.
    2. Clinet, Simon & Potiron, Yoann, 2019. "Testing if the market microstructure noise is fully explained by the informational content of some variables from the limit order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 289-337.
    3. Xinwei Feng & Lidan He & Zhi Liu, 2022. "Large Deviation Principles of Realized Laplace Transform of Volatility," Journal of Theoretical Probability, Springer, vol. 35(1), pages 186-208, March.
    4. Hsu, Ching-Chi & Chau, Ka Yin & Chien, FengSheng, 2023. "Natural resource volatility and financial development during Covid-19: Implications for economic recovery," Resources Policy, Elsevier, vol. 81(C).
    5. Simon Clinet & Yoann Potiron, 2021. "Estimation for high-frequency data under parametric market microstructure noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 649-669, August.
    6. Li, Jia & Todorov, Viktor & Tauchen, George, 2017. "Adaptive estimation of continuous-time regression models using high-frequency data," Journal of Econometrics, Elsevier, vol. 200(1), pages 36-47.
    7. Randolf Altmeyer & Markus Bibinger, 2014. "Functional stable limit theorems for efficient spectral covolatility estimators," SFB 649 Discussion Papers SFB649DP2014-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Camponovo, Lorenzo & Matsushita, Yukitoshi & Otsu, Taisuke, 2019. "Empirical likelihood for high frequency data," LSE Research Online Documents on Economics 100320, London School of Economics and Political Science, LSE Library.
    9. Zhang, Junpeng & Pang, Deliang & Yang, Leijing & Ouyang, Wenjun, 2023. "Risk and synergy of multinational enterprise mergers and acquisitions under the background of the COVID-19 pandemic," Economic Analysis and Policy, Elsevier, vol. 78(C), pages 718-729.

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