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A family of autoregressive conditional duration models

  • Fernandes, Marcelo
  • Grammig, Joachim

This paper develops a family of autoregressive conditional duration (ACD) models that encompasses most specifications in the literature. The nesting relies on a Box-Cox transformation with shape parameter [delta] to the conditional duration process anda possibly asymmetric shocks impact curve. We establish conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and [beta]-mixing property with exponential decay. We next derive moment recursion relations and the autocovariance function of the power [delta] of the duration process. Finally, we assess the practical usefulness of our family of ACD models using NYSE price duration data on the IBM stock. While the in-sample results warrant the extra flexibility provided either by the Box-Cox transformation or by the asymmetric response to shocks, we find no specification that entails satisfactory out-of-sample performance.

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Paper provided by FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil) in its series Economics Working Papers (Ensaios Economicos da EPGE) with number 501.

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Date of creation: 05 Oct 2003
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Handle: RePEc:fgv:epgewp:501
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  1. Engle, Robert F. & Russell, Jeffrey R., 1997. "Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 187-212, June.
  2. Dinh Tuan, Pham, 1986. "The mixing property of bilinear and generalised random coefficient autoregressive models," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 291-300, December.
  3. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
  4. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
  5. He, Changli & Teräsvirta, Timo & Malmsten, Hans, 1999. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models," SSE/EFI Working Paper Series in Economics and Finance 345, Stockholm School of Economics.
  6. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Centre de Recherche en Economie et Statistique.
  7. Marcelo Fernandes & Joachim Grammig, 2000. "Non-Parametric Specification Tests For Conditional Duration Models," Computing in Economics and Finance 2000 40, Society for Computational Economics.
  8. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Alfonso Dufour & Robert F Engle, 2000. "The ACD Model: Predictability of the Time Between Concecutive Trades," ICMA Centre Discussion Papers in Finance icma-dp2000-05, Henley Business School, Reading University.
  10. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.
  11. Luc BAUWENS & Pierre GIOT, 2000. "The Logarithmic ACD Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks," Annales d'Economie et de Statistique, ENSAE, issue 60, pages 117-149.
  12. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  13. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," CORE Discussion Papers 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. 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.
  15. repec:att:wimass:9520 is not listed on IDEAS
  16. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
  17. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2001. "A nonlinear autoregressive conditional duration model with applications to financial transaction data," Journal of Econometrics, Elsevier, vol. 104(1), pages 179-207, August.
  18. GIOT, Pierre, 1999. "Time transformations, intraday data and volatility models," CORE Discussion Papers 1999044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  19. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  20. Eric Ghysels & Christian Gourieroux & Joanna Jasiak, 1997. "Stochastic Volatility Duration Models," Working Papers 97-46, Centre de Recherche en Economie et Statistique.
  21. He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, vol. 18(04), pages 868-885, August.
  22. Easley, David & O'Hara, Maureen, 1992. " Time and the Process of Security Price Adjustment," Journal of Finance, American Finance Association, vol. 47(2), pages 576-605, June.
  23. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
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