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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 Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2001036.

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Date of creation: 00 Aug 2001
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Handle: RePEc:cor:louvco:2001036
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  1. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
  2. Luc Bauwens & Pierre Giot & Joachim Grammig & David Veredas, 2004. "A comparison of financial duration models via density forecast," ULB Institutional Repository 2013/136218, ULB -- Universite Libre de Bruxelles.
  3. 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.
  4. 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).
  5. Fernandes, Marcelo & Grammig, Joachim, 2003. "Nonparametric specification tests for conditional duration models," Economics Working Papers (Ensaios Economicos da EPGE) 502, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  6. Changli He & Timo Terasvirta & Hans Malmsten, 1999. "Fourth Moment Structure of a Family of First-Order Exponential GARCH Models," Research Paper Series 29, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. 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.
  8. repec:att:wimass:9520 is not listed on IDEAS
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Eric Ghysels & Christian Gourieroux & Joanna Jasiak, 1997. "Stochastic Volatility Duration Models," Working Papers 97-46, Centre de Recherche en Economie et Statistique.
  16. BAUWENS, Luc & GIOT, Pierre, . "The logarithmic ACD model: an application to the bid-ask quote process of three NYSE stocks," CORE Discussion Papers RP 1497, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. 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.
  18. 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.
  19. 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).
  20. 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.
  21. 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.
  22. 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.
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