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Estimating Quadratic VariationConsistently in thePresence of Correlated MeasurementError

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Author Info
Ilze Kalnina
Oliver Linton

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Abstract

We propose an econometric model that captures the e¤ects of marketmicrostructure on a latent price process. In particular, we allow for correlationbetween the measurement error and the return process and we allow themeasurement error process to have a diurnal heteroskedasticity. Wepropose a modification of the TSRV estimator of quadratic variation. Weshow that this estimator is consistent, with a rate of convergence thatdepends on the size of the measurement error, but is no worse than n1=6.We investigate in simulation experiments the finite sample performance ofvarious proposed implementations.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2006/509.

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Date of creation: Oct 2006
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Handle: RePEc:cep:stiecm:/2006/509

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Related research
Keywords: Endogenous noise; Market Microstructure; Realised Volatility; Semimartingale;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

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  1. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March. [Downloadable!] (restricted)
  2. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  3. 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 2006fe05, Oxford Financial Research Centre. [Downloadable!]
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  4. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 18(2), pages 351-416. [Downloadable!] (restricted)
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  5. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843 Elsevier. [Downloadable!] (restricted)
  6. McInish, Thomas H & Wood, Robert A, 1992. " An Analysis of Intraday Patterns in Bid/Ask Spreads for NYSE Stocks," Journal of Finance, American Finance Association, vol. 47(2), pages 753-64, June. [Downloadable!] (restricted)
  7. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society. [Downloadable!]
  8. 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. [Downloadable!] (restricted)
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  9. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  10. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2005. "Edgeworth Expansions for Realized Volatility and Related Estimators," NBER Technical Working Papers 0319, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  11. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001. [Downloadable!]
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  12. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," Economics Papers 2005-W16, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  13. Ait-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2005. "Ultra high frequency volatility estimation with dependent microstructure noise," Discussion Paper Series 1: Economic Studies 2005,30, Deutsche Bundesbank, Research Centre. [Downloadable!]
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  14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. Andersen, Torben G. & Bollerslev, Tim & Cai, Jun, 2000. "Intraday and interday volatility in the Japanese stock market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 10(2), pages 107-130, June. [Downloadable!] (restricted)
  17. Gottlieb, Gary & Kalay, Avner, 1985. " Implications of the Discreteness of Observed Stock Prices," Journal of Finance, American Finance Association, vol. 40(1), pages 135-53, March. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semin-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Economics Series Working Papers 397, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Subsampling realised kernels," Economics Papers 2006-W10, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
    Other versions:
  3. Ilze Kalnina & Oliver Linton, 2007. "Inference about Realized Volatility using Infill Subsampling," STICERD - Econometrics Paper Series /2007/523, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  4. Neil Shephard & Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 264, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
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