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

  • Ingmar Nolte

    ()

    (Warwick Business School,FERC, CoFE)

  • Valeri Voev

    ()

    (University of Aarhus, CoFE and CREATES)

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 a joint inference on integrated volatility (IV), noise moments and price-noise relations. In the iid noise case we derive the asymptotic variance of the regression parameter estimating the IV, show that it is consistent and compare its asymptotic efficiency against alternative consistent IV measures. In case of noise which is correlated with the efficient return process, we postulate a new “asymptotically increasing” type of dependence and analyze its ability to cope with the empirically observed price-noise dependence in quote data. In the empirical section of the paper we apply the LS methodology to estimate the integrated volatility as well as the noise properties of 25 liquid stocks both with midquote and transaction price data. We find that while iid noise is an oversimplification, its non-iid characteristics have a decidedly negligible effect on volatility estimation within our framework, for which we provide a sound theoretical reason. In terms of noise-price endogeneity, we are not able o find empirical support for simple ad hoc theoretical models and we provide an alternative explanation for the observed patterns in midquote data, based on market microstructure theory.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-16.

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Length: 40
Date of creation: 27 Apr 2009
Date of revision:
Handle: RePEc:aah:create:2009-16
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," CREATES Research Papers 2008-63, School of Economics and Management, University of Aarhus.
  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. 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.
  4. 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.
  5. Roel Oomen, 2004. "Properties of Bias Corrected Realized Variance Under Alternative Sampling Schemes," Working Papers wp04-15, Warwick Business School, Finance Group.
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  7. 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.
  8. repec:oxf:wpaper:264 is not listed on IDEAS
  9. Lo, Andrew W. & Craig MacKinlay, A., 1990. "An econometric analysis of nonsynchronous trading," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 181-211.
  10. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers 185, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. 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 C1-C32, November.
  12. 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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