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

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  • Ingmar Nolte

    ()
    (Warwick Business School,FERC, CoFE)

  • Valeri Voev

    ()
    (University of Aarhus, CoFE and CREATES)

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 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 to 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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Bibliographic Info

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

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Web page: http://www.econ.au.dk/afn/

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Keywords: High frequency data; Subsampling; Realized volatility; Market microstructure;

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  1. 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, Royal Statistical Society, vol. 64(2), pages 253-280.
  2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, Econometric Society, vol. 71(2), pages 579-625, March.
  3. 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, School of Economics and Management, University of Aarhus 2008-63, School of Economics and Management, University of Aarhus.
  4. Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series, Oxford Financial Research Centre 2006fe05, Oxford Financial Research Centre.
  5. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 185, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 79(3), pages 655-692, March.
  7. Roel Oomen, 2004. "Properties of Bias Corrected Realized Variance Under Alternative Sampling Schemes," Working Papers, Warwick Business School, Finance Group wp04-15, Warwick Business School, Finance Group.
  8. repec:oxf:wpaper:264 is not listed on IDEAS
  9. Andrew W. Lo & A. Craig MacKinlay, 1991. "An Econometric Analysis of Nonsynchronous Trading," NBER Working Papers 2960, National Bureau of Economic Research, Inc.
  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, Royal Economic Society, vol. 12(3), pages C1-C32, November.
  11. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 24, pages 127-161, April.
  12. 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, American Statistical Association, vol. 100, pages 1394-1411, December.
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Cited by:
  1. Roxana Halbleib & Valeri Voev, 2012. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Paper Series of the Department of Economics, University of Konstanz, Department of Economics, University of Konstanz 2012-30, Department of Economics, University of Konstanz.
  2. Selma Chaker, 2013. "Volatility and Liquidity Costs," Working Papers, Bank of Canada 13-29, Bank of Canada.
  3. Yuta Koike, 2013. "Limit Theorems for the Pre-averaged Hayashi-Yoshida Estimator with Random Sampling," Global COE Hi-Stat Discussion Paper Series, Institute of Economic Research, Hitotsubashi University gd12-276, Institute of Economic Research, Hitotsubashi University.

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