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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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Suggested Citation

  • Ingmar Nolte & Valeri Voev, 2009. "Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise," Working Papers wp09-02, Warwick Business School, Finance Group.
  • Handle: RePEc:wbs:wpaper:wp09-02
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    References listed on IDEAS

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    1. Roel C. A. Oomen, 2005. "Properties of Bias-Corrected Realized Variance Under Alternative Sampling Schemes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 555-577.
    2. 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.
    3. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
    4. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    5. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    6. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
    7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    8. repec:oxf:wpaper:264 is not listed on IDEAS
    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.
    10. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    11. Lo, Andrew W. & Craig MacKinlay, A., 1990. "An econometric analysis of nonsynchronous trading," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 181-211.
    12. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
    13. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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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. Roxana Halbleib & Valerie Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Papers ECARES ECARES 2011-002, ULB -- Universite Libre de Bruxelles.
    3. Selma Chaker, 2013. "Volatility and Liquidity Costs," Staff Working Papers 13-29, Bank of Canada.
    4. Roxana Halbleib & Valeri Voev, 2016. "Forecasting Covariance Matrices: A Mixed Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(2), pages 383-417.

    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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