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Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics

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  • Ole E. Barndorff-Nielsen
  • Neil Shephard

Abstract

This paper analyses multivariate high frequency financial data using realised covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis and covariance. It will be based on a fixed interval of time (e.g. a day or week), allowing the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions and covariances change through time. In particular we provide confidence intervals for each of these quantities.

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Bibliographic Info

Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2002fe03.

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Date of creation: 2002
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Handle: RePEc:sbs:wpsefe:2002fe03

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Web page: http://www.finance.ox.ac.uk
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  1. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Estimating quadratic variation using realised variance," Economics Series Working Papers 2001-W20, University of Oxford, Department of Economics.
  2. 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.
  3. Nour Meddahi, 2000. "Temporal Aggregation of Volatility Models," Econometric Society World Congress 2000 Contributed Papers 1903, Econometric Society.
  4. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
  5. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
  7. Neil Shephard & Siddhartha Chib, 1999. "Analysis of High Dimensional Multivariate Stochastic Volatility Models," Economics Series Working Papers 1999-W18, University of Oxford, Department of Economics.
  8. Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers 96.406, Toulouse - GREMAQ.
  9. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  10. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  11. MEDDAHI, Nour, 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Universite de Montreal, Departement de sciences economiques.
  12. 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.
  13. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  14. Torben Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," NBER Working Papers 6961, National Bureau of Economic Research, Inc.
  15. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-74, January.
  16. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford.
  17. MEDDAHI, Nour & RENAULT, Éric, 1998. "Aggregations and Marginalization of GARCH and Stochastic Volatility Models," Cahiers de recherche 9818, Universite de Montreal, Departement de sciences economiques.
  18. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  19. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
  20. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Realised power variation and stochastic volatility models," Economics Series Working Papers 2001-W18, University of Oxford, Department of Economics.
  21. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
  22. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  23. Andreou, Elena & Ghysels, Eric, 2002. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation, and Empirical Results," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 363-76, July.
  24. 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.
  25. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September.
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