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GARCH Parameter Estimation Using High-Frequency Data

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  • Marcel P. Visser

Abstract

A standard procedure for obtaining parameter values of a GARCH model for financial volatility is the quasi maximum likelihood estimator (QMLE) based on daily close-to-close returns. This paper generalizes the QMLE based on daily returns to a QMLE based on intraday high-frequency data. Volatility proxies, such as the realized volatility or the daily high--low range, are used for estimating the parameters of discrete-time GARCH models. Empirical analysis of the S&P 500 index tick data shows that a well-chosen proxy may reduce the variances of the estimators of the GARCH(1,1) autoregression parameters by a factor 20. C14, C22, C51, G1 Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

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Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 9 (2011)
Issue (Month): 1 (Winter)
Pages: 162-197

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Handle: RePEc:oup:jfinec:v:9:y:2011:i:1:p:162-197

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  1. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 61(1), pages 43-76, July.
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  5. Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 81(1), pages 193-221, November.
  6. Fiorentini,G. & Calzolari,G. & Panattoni,L., 1995. "Analytic Derivatives and the Computation of Garch Estimates," Papers, Centro de Estudios Monetarios Y Financieros- 9519, Centro de Estudios Monetarios Y Financieros-.
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  8. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, Econometric Society, vol. 64(3), pages 575-96, May.
  9. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  10. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 129(1-2), pages 121-138.
  11. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," CIRANO Working Papers, CIRANO 2004s-19, CIRANO.
  12. de Vilder, Robin G. & Visser, Marcel P., 2007. "Volatility Proxies for Discrete Time Models," MPRA Paper 4917, University Library of Munich, Germany.
  13. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 909-27, July.
  14. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(01), pages 29-52, March.
  15. Lumsdaine, Robin L, 1995. "Finite-Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 13(1), pages 1-10, January.
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Cited by:
  1. Piotr Fiszeder & Grzegorz Perczak, 2013. "A new look at variance estimation based on low, high and closing prices taking into account the drift," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 456-481, November.
  2. Peter R. Hansen & Asger Lunde & Valeri Voev, 2010. "Realized Beta GARCH: A Multivariate GARCH Model with Realized Measures of Volatility and CoVolatility," CREATES Research Papers, School of Economics and Management, University of Aarhus 2010-74, School of Economics and Management, University of Aarhus.
  3. Peter Reinhard Hansen & Zhuo Huang, 2012. "Exponential GARCH Modeling with Realized Measures of Volatility," CREATES Research Papers, School of Economics and Management, University of Aarhus 2012-44, School of Economics and Management, University of Aarhus.
  4. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2011. "Financial Risk Measurement for Financial Risk Management," CREATES Research Papers, School of Economics and Management, University of Aarhus 2011-37, School of Economics and Management, University of Aarhus.
  5. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2013. "Which continuous-time model is most appropriate for exchange rates?," Working Papers, Federal Reserve Bank of St. Louis 2013-024, Federal Reserve Bank of St. Louis.
  6. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, . "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers, School of Economics and Management, University of Aarhus 2010-13, School of Economics and Management, University of Aarhus.
  7. Visser, Marcel P., 2008. "Forecasting S&P 500 Daily Volatility using a Proxy for Downward Price Pressure," MPRA Paper 11100, University Library of Munich, Germany.
  8. Hecq Alain & Laurent Sébastien & Palm Franz, 2011. "Common intraday periodicity," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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