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Properties of Estimates of Daily GARCH Parameters Basaed on Intra-Day Observations

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  • John Galbraith

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  • Victoria Zinde-Walsh

Abstract

We consider estimates of the parameters of GARCH models of daily financial returns, obtained using intra-day (high-frequency) returns data to estimate the daily conditional volatility.Two potential bases for estimation are considered. One uses aggregation of high-frequency Quasi- ML estimates, using aggregation results of Drost and Nijman (1993). The other uses the integrated volatility of Andersen and Bollerslev (1998), and obtains coefficients from a model estimated by LAD or OLS, in the former case providing consistency and asymptotic normality in some cases where moments of the volatility estimation error may not exist. In particular, we consider estimation in this way of an ARCH approximation, and obtain GARCH parameters by a method related to that of Galbraith and Zinde-Walsh (1997) for ARMA processes. We offer some simulation evidence on small-sample performance, and characterize the gains relative to standard quasi-ML estimates based on daily data alone. Nous considérons les estimés des paramètres des modèles GARCH pour les rendements financiers journaliers, qui sont obtenus à l'aide des données intra-jour (haute fréquence) pour estimer la volatilité journalière. Deux bases potentielles sont evaluées. La première est fondée sur l'aggrégation des estimés quasi-vraisemblance-maximale, en profitant des résultats de Drost et Nijman (1993). L'autre utilise la volatilité integrée de Andersen et Bollerslev (1998), et obtient les coefficients d'un modèle estimé par LAD ou MCO; la première méthode résiste mieux à la possibilité de non-existence des moments de l'erreur en estimation de volatilité. En particulier, nous considérons l'estimation par approximation ARCH, et nous obtenons les paramètres par une méthode liée à celle de Galbraith et Zinde-Walsh (1997) pour les processus ARMA. Nous offrons des résultats provenant des simulations sur la performance des méthodes en échantillons finis, et nous décrivons les atouts relatifs à l'estimation standard de quasi-VM basée uniquement sur les données journalières.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2001s-15.

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Date of creation: 01 Feb 2001
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Handle: RePEc:cir:cirwor:2001s-15

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Keywords: GARCH; high frequency data; integrated volatility; LAD; GARCH; données haute fréquence; volatilité intégrée; LAD;

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  1. 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.
  2. John M. Maheu & Thomas H. McCurdy, 2002. "Nonlinear Features of Realized FX Volatility," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 668-681, November.
  3. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  5. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  6. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
  7. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  8. Nour Meddahi, 2000. "Temporal Aggregation of Volatility Models," Econometric Society World Congress 2000 Contributed Papers 1903, Econometric Society.
  9. Nelson, Daniel B. & Foster, Dean P., 1995. "Filtering and forecasting with misspecified ARCH models II : Making the right forecast with the wrong model," Journal of Econometrics, Elsevier, vol. 67(2), pages 303-335, June.
  10. 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.
  11. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
  12. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
  13. Bollen, B. & Inder, B., 1998. "A General Volatility Framework and the Generalised Historical Volatility Estimator," Monash Econometrics and Business Statistics Working Papers 10/98, Monash University, Department of Econometrics and Business Statistics.
  14. 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.
  15. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(05), pages 912-951, October.
  16. 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.
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Cited by:
  1. MEDDAHI, Nour, 2002. "ARMA Representation of Integrated and Realized Variances," Cahiers de recherche 2002-20, Universite de Montreal, Departement de sciences economiques.
  2. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Nour Meddahi, 2001. "A Theoretical Comparison Between Integrated andRealized Volatilities / A Theoretical Comparison Between Integrated and Realized Volatilities," CIRANO Working Papers 2001s-71, CIRANO.
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Realised power variation and stochastic volatility models," Economics Papers 2001-W18, Economics Group, Nuffield College, University of Oxford.

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