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Subsampling realised kernels

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  • Barndorff-Nielsen, Ole E.
  • Hansen, Peter Reinhard
  • Lunde, Asger
  • Shephard, Neil

Abstract

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 160 (2011)
Issue (Month): 1 (January)
Pages: 204-219

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Handle: RePEc:eee:econom:v:160:y:2011:i:1:p:204-219

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

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Keywords: Long run variance estimator Market frictions Quadratic variation Realised kernel Realised variance Subsampling;

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  1. Ilze Kalnina & Oliver Linton, 2006. "Estimating quadratic variation consistently in the presence of correlated measurement error," LSE Research Online Documents on Economics 4413, London School of Economics and Political Science, LSE Library.
  2. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
  3. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society.
  4. Yacine Ait-Sahalia & Per A. Mykland & Lan Zhang, 2005. "Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise," NBER Working Papers 11380, National Bureau of Economic Research, Inc.
  5. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
  6. 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.
  7. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 339-369.
  8. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 525-554.
  9. 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.
  10. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  11. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 219-237, April.
  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. 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.
  14. Ilze Kalnina & Oliver Linton, 2006. "Estimating Quadratic VariationConsistently in thePresence of Correlated MeasurementError," STICERD - Econometrics Paper Series /2006/509, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  15. Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Series Working Papers 2005-FE-09, University of Oxford, Department of Economics.
  16. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
  17. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, September.
  18. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
  19. Kalnina, Ilze & Linton, Oliver, 2008. "Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error," Journal of Econometrics, Elsevier, vol. 147(1), pages 47-59, November.
  20. 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.
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