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Least Squares Inference on Integrated Volatility and the Relationship Between Efficient Prices and Noise

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  • Ingmar Nolte
  • Valeri Voev

Abstract

The expected value of sums of squared intraday returns (realized variance) gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for joint inference on integrated variance (), noise moments, and price-noise relations. In the iid noise case, we derive the asymptotic variance of the and noise variance estimators and show that they are consistent. The joint estimation approach is particularly attractive as it reveals important characteristics of the noise process which can be related to liquidity and market efficiency. The analysis of dependence between the price and noise processes provides an often missing link to market microstructure theory. We find substantial differences in the noise characteristics of trade and quote data arising from the effect of distinct market microstructure frictions. This article has supplementary material online.

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  • Ingmar Nolte & Valeri Voev, 2012. "Least Squares Inference on Integrated Volatility and the Relationship Between Efficient Prices and Noise," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 94-108.
    • Handle: RePEc:taf:jnlbes:v:30:y:2012:i:1:p:94-108
    DOI: 10.1080/10473289.2011.637876
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    Cited by:

    1. Yuta Koike, 2013. "Limit Theorems for the Pre-averaged Hayashi-Yoshida Estimator with Random Sampling," Global COE Hi-Stat Discussion Paper Series gd12-276, Institute of Economic Research, Hitotsubashi University.
    2. Li, Yifan & Nolte, Ingmar & Vasios, Michalis & Voev, Valeri & Xu, Qi, 2022. "Weighted Least Squares Realized Covariation Estimation," Journal of Banking & Finance, Elsevier, vol. 137(C).
    3. Varneskov, Rasmus & Voev, Valeri, 2013. "The role of realized ex-post covariance measures and dynamic model choice on the quality of covariance forecasts," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 83-95.
    4. Vladimír Holý & Petra Tomanová, 2023. "Streaming Approach to Quadratic Covariation Estimation Using Financial Ultra-High-Frequency Data," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 463-485, June.
    5. Selma Chaker, 2013. "Volatility and Liquidity Costs," Staff Working Papers 13-29, Bank of Canada.
    6. Vladim'ir Hol'y & Petra Tomanov'a, 2020. "Streaming Approach to Quadratic Covariation Estimation Using Financial Ultra-High-Frequency Data," Papers 2003.13062, arXiv.org, revised Dec 2021.

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