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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.

Suggested Citation

  • Ingmar Nolte & Valeri Voev, 2011. "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, April.
    • Handle: RePEc:taf:jnlbes:v:30:y:2011:i:1:p:94-108
    DOI: 10.1080/10473289.2011.637876
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    9. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
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    Cited by:

    1. Roxana Halbleib & Valerie Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Papers ECARES ECARES 2011-002, ULB -- Universite Libre de Bruxelles.
    2. 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.
    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. Roxana Halbleib & Valeri Voev, 2016. "Forecasting Covariance Matrices: A Mixed Approach," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 383-417.
    5. 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.
    6. Selma Chaker, 2013. "Volatility and Liquidity Costs," Staff Working Papers 13-29, Bank of Canada.

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    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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