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Garch Parameter Estimation Using High-Frequency Data

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  • Visser, Marcel P.

Abstract

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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Bibliographic Info

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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Keywords: volatility estimation; quasi maximum likelihood; volatility proxy; Gaussian QMLE; log-Gaussian QMLE; autoregressive conditional heteroscedasticity;

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References

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  1. Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
  2. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, Elsevier, vol. 131(1-2), pages 3-27.
  3. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 909-27, July.
  4. Drost, F.C. & Klaassen, C.A.J., 1996. "Efficient Estimation in Semiparametric GARCH Models," Discussion Paper, Tilburg University, Center for Economic Research 1996-38, Tilburg University, Center for Economic Research.
  5. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, Elsevier, vol. 131(1-2), pages 59-95.
  6. 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.
  7. 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.
  8. 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.
  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. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, American Finance Association, vol. 57(3), pages 1047-1091, 06.
  11. de Vilder, Robin G. & Visser, Marcel P., 2007. "Volatility Proxies for Discrete Time Models," MPRA Paper 4917, University Library of Munich, Germany.
  12. 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.
  13. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, Elsevier, vol. 4(2-3), pages 115-158, June.
  14. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 129(1-2), pages 121-138.
  15. 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.
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Citations

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Cited by:
  1. Peter Reinhard Hansen & Asger Lunde & Valeri Voev, 2012. "Realized Beta GARCH: A Multivariate GARCH Model with Realized Measures of Volatility and Covolatility," Global COE Hi-Stat Discussion Paper Series, Institute of Economic Research, Hitotsubashi University gd12-269, Institute of Economic Research, Hitotsubashi University.
  2. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2011. "Financial Risk Measurement for Financial Risk Management," PIER Working Paper Archive 11-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  3. Peter Reinhard Hansen & Zhuo Huang, 2012. "Exponential GARCH Modeling with Realized Measures of Volatility," Economics Working Papers, European University Institute ECO2012/26, European University Institute.
  4. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, . "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, 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. Alain Hecq & Sébastien Laurent & Franz C. Palm, 2011. "Common Intraday Periodicity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(2), pages 325-353, 2012 20 1.
  7. 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.
  8. 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.

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