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GARCH and Irregularly Spaced Data

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  • Meddahi, N.
  • Renault, E.
  • Werker, B.J.M.

    (Tilburg University, Center for Economic Research)

Abstract

An exact discretization of continuous time stochastic volatility processes observed at irregularly spaced times is used to give insights on how a coherent GARCH model can be specified for such data. The relation of our approach with those in the existing literature is studied.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2003-27.

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Date of creation: 2003
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Handle: RePEc:dgr:kubcen:200327

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Web page: http://center.uvt.nl

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Keywords: volatility; continuous time model; garch models; time models; exact discretization;

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References

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  1. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Nour Meddahi, 2000. "Temporal Aggregation of Volatility Models," Econometric Society World Congress 2000 Contributed Papers 1903, Econometric Society.
  4. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  5. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO.
  6. Werker, B.J.M. & Drost, F.C., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-72561, Tilburg University.
  7. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
  8. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  9. Renault, E. & Werker, B.J.M., 2004. "Stochatic Volatility Models with Transaction Time Risk," Discussion Paper 2004-24, Tilburg University, Center for Economic Research.
  10. Ghysels Eric & Jasiak Joanna, 1998. "GARCH for Irregularly Spaced Financial Data: The ACD-GARCH Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(4), pages 1-19, January.
  11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
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Citations

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Cited by:
  1. Dionne, Georges & Duchesne, Pierre & Pacurar, Maria, 2009. "Intraday Value at Risk (IVaR) using tick-by-tick data with application to the Toronto Stock Exchange," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 777-792, December.
  2. Li, Yingying & Zhang, Zhiyuan & Zheng, Xinghua, 2013. "Volatility inference in the presence of both endogenous time and microstructure noise," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2696-2727.
  3. Luc Bauwens & Nikolaus Hautsch, 2007. "Modelling Financial High Frequency Data Using Point Processes," SFB 649 Discussion Papers SFB649DP2007-066, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Renault, Eric & van der Heijden, Thijs & Werker, Bas J.M., 2014. "The dynamic mixed hitting-time model for multiple transaction prices and times," Journal of Econometrics, Elsevier, vol. 180(2), pages 233-250.
  5. Hautsch, Nikolaus, 2007. "Capturing common components in high-frequency financial time series: A multivariate stochastic multiplicative error model," CFS Working Paper Series 2007/25, Center for Financial Studies (CFS).
  6. Renault, Eric & Werker, Bas J.M., 2011. "Causality effects in return volatility measures with random times," Journal of Econometrics, Elsevier, vol. 160(1), pages 272-279, January.
  7. Maria Pacurar, 2008. "Autoregressive Conditional Duration Models In Finance: A Survey Of The Theoretical And Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 711-751, 09.

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