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Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise

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  • Mancino, M.E.
  • Sanfelici, S.

Abstract

The finite sample properties of the Fourier estimator of integrated volatility under market microstructure noise are studied. Analytic expressions for the bias and the mean squared error (MSE) of the contaminated estimator are derived. These formulae can be practically used to design optimal MSE-based estimators, which are very robust and efficient in the presence of noise. Moreover an empirical analysis based on a simulation study and on high-frequency logarithmic prices of the Italian stock index futures (FIB30) validates the theoretical results.

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File URL: http://www.sciencedirect.com/science/article/B6V8V-4PC3VCH-1/1/647b07afe63b8b088680059b2d67a5db
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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2008)
Issue (Month): 6 (February)
Pages: 2966-2989

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Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:2966-2989

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Web page: http://www.elsevier.com/locate/csda

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References

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  1. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Subsampling realised kernels," Journal of Econometrics, Elsevier, vol. 160(1), pages 204-219, January.
  2. Nielsen, Morten Ørregaard & Frederiksen, Per, 2008. "Finite sample accuracy and choice of sampling frequency in integrated volatility estimation," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 265-286, March.
  3. Barucci, Emilio & Reno, Roberto, 2002. "On measuring volatility and the GARCH forecasting performance," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 12(3), pages 183-200, July.
  4. Christian T. Brownlees & Giampiero Gallo, 2006. "Financial Econometric Analysis at Ultra–High Frequency: Data Handling Concerns," Econometrics Working Papers Archive wp2006_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  5. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
  6. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
  7. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
  8. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Papers 2006-W03, Economics Group, Nuffield College, University of Oxford.
  9. Harris, Lawrence, 1991. "Stock Price Clustering and Discreteness," Review of Financial Studies, Society for Financial Studies, vol. 4(3), pages 389-415.
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  11. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  12. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  13. 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.
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Citations

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Cited by:
  1. Flavia Barsotti & Simona Sanfelici, 2012. "Microstructure effect on firm’s volatility risk," Working Papers - Mathematical Economics 2012-05, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  2. S. Sanfelici & M. E. Mancino, 2008. "Covariance estimation via Fourier method in the presence of asynchronous trading and microstructure noise," Economics Department Working Papers 2008-ME01, Department of Economics, Parma University (Italy).
  3. Imma Valentina Curato, 2013. "Fourier estimation of stochastic leverage using high frequency data," Working Papers - Mathematical Economics 2013-04, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  4. Mancino Maria Elvira & Simona Sanfelici, 2009. "Covariance estimation and dynamic asset allocation under microstructure effects via Fourier methodology," Working Papers - Mathematical Economics 2009-09, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  5. Cecilia Mancini & Vanessa Mattiussi & Roberto Reno', 2012. "Spot Volatility Estimation Using Delta Sequences," Working Papers - Mathematical Economics 2012-10, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  6. Clément, Emmanuelle & Gloter, Arnaud, 2011. "Limit theorems in the Fourier transform method for the estimation of multivariate volatility," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1097-1124, May.
  7. Rasmus Tangsgaard Varneskov, 2011. "Generalized Flat-Top Realized Kernel Estimation of Ex-Post Variation of Asset Prices Contaminated by Noise," CREATES Research Papers 2011-31, School of Economics and Management, University of Aarhus.
  8. Maria Elvira Mancino & Simona Sanfelici, 2011. "Estimation of Quarticity with High Frequency Data," Working Papers - Mathematical Economics 2011-06, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa, revised Jan 2012.
  9. Borovkova, Svetlana & Permana, Ferry J., 2009. "Implied volatility in oil markets," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2022-2039, April.
  10. Wang, Fangfang, 2014. "Optimal design of Fourier estimator in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 708-722.

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