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Garch Parameter Estimation Using High-Frequency Data

  • Visser, Marcel P.

Estimation of the parameters of Garch models for financial data is typically based on daily close-to-close returns. This paper shows that the efficiency of the parameter estimators may be greatly improved by using volatility proxies based on intraday data. The paper develops a Garch quasi maximum likelihood estimator (QMLE) based on these proxies. Examples of such proxies are the realized volatility and the intraday high-low range. Empirical analysis of the S&P 500 index tick data shows that the use of a suitable proxy may reduce the variances of the estimators of the Garch autoregression parameters by a factor 20.

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File URL: http://mpra.ub.uni-muenchen.de/9076/1/MPRA_paper_9076.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9076.

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Date of creation: 10 Jun 2008
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Handle: RePEc:pra:mprapa:9076
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  1. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," CIRANO Working Papers 2004s-19, CIRANO.
  2. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
  3. de Vilder, Robin G. & Visser, Marcel P., 2007. "Volatility Proxies for Discrete Time Models," MPRA Paper 4917, University Library of Munich, Germany.
  4. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, 06.
  5. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  7. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  8. Drost, F.C. & Klaassen, C.A.J., 1997. "Efficient estimation in semiparametric GARCH models," Other publications TiSEM c7de3f1c-c456-433e-a1c6-2, Tilburg University, School of Economics and Management.
  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. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
  11. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  12. 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, vol. 64(3), pages 575-96, May.
  13. Drost, F.C. & Klaassen, C.A.J., 1996. "Efficient Estimation in Semiparametric GARCH Models," Discussion Paper 1996-38, Tilburg University, Center for Economic Research.
  14. 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, vol. 13(1), pages 1-10, January.
  15. Fiorentini,G. & Calzolari,G. & Panattoni,L., 1995. "Analytic Derivatives and the Computation of Garch Estimates," Papers 9519, Centro de Estudios Monetarios Y Financieros-.
  16. 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.
  17. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
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