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A family of autoregressive conditional duration models

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Author Info
FERNANDES, Marcelo
GRAMMIG, Joachim

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Abstract

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: 01 Aug 2001
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Handle: RePEc:cor:louvco:2001036

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Related research
Keywords: Asymmetry; Box-Cox transformation; mixing property; price duration; shocks impact curve; stationarity;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. 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.
  2. 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). [Downloadable!]
  3. 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. [Downloadable!]
  4. Fernandes, M. & Grammig, J., 2000. "Non-Parametric Specification Tests for Conditional Duration Models," Economics Working Papers eco2000/4, European University Institute.
    Other versions:
  5. 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.
  6. 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. [Downloadable!] (restricted)
  7. Ghysels, Eric & Gourieroux, Christian & Jasiak, Joann, 2004. "Stochastic volatility duration models," Journal of Econometrics, Elsevier, vol. 119(2), pages 413-433, April. [Downloadable!] (restricted)
  8. 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.
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  10. Jean -Luc Prigent ; Olivier Renault ; Olivier Scaillet, . "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Centre de Recherche en Economie et Statistique. [Downloadable!]
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  11. 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). [Downloadable!]
  12. 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. [Downloadable!] (restricted)
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  13. 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. [Downloadable!]
  14. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
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  15. 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, ADRES, issue 60, pages 06, Octobre-D. [Downloadable!]
  16. 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. [Downloadable!] (restricted)
  17. C. He & Timo Terasvirta & H. 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.
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  18. 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. [Downloadable!]
  19. 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. [Downloadable!] (restricted)
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  20. Pedro de Lima, 1996. "Nuisance parameter free properties of correlation integral based statistics," Econometric Reviews, Taylor and Francis Journals, vol. 15(3), pages 237-259. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Nikolaus Hautsch, 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. [Downloadable!]
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  2. repec:bep:sndecm:11:2007:2:1377-1377 is not listed on IDEAS
  3. BAUWENS, Luc & HAUTSCH, Nikolaus, 2003. "Dynamic latent factor models for intensity processes," CORE Discussion Papers 2003103, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  4. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V. K., 2006. "Nonparametric density estimation for positive time series," CORE Discussion Papers 2006085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  5. Frank Gerhard & Nikolaus Hautsch, 2006. "A Dynamic Semiparametric Proportional Hazard Model," FRU Working Papers 2006/05, University of Copenhagen. Department of Economics. Finance Research Unit. [Downloadable!]
  6. Laurini, Márcio P. & Furlani, Luiz G. C. & Portugual, Marcelo S., 2008. "Empirical Market Microstructure: An Analysis Of The Brl/Us$ Exchange Rate Market Using High-Frequency Data," Ibmec Working Papers wpe_101, Ibmec Working Paper, Ibmec São Paulo. [Downloadable!]
  7. Wing Lon NG, 2004. "Duration and Order Type Clusters," Econometric Society 2004 Far Eastern Meetings 730, Econometric Society. [Downloadable!]
  8. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
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  9. Nikolaus Hautsch, 2002. "Modelling Intraday Trading Activity Using Box-Cox-ACD Models," CoFE Discussion Paper 02-05, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
  10. Nikolaus Hautsch, 2006. "Testing the Conditional Mean Function of Autoregressive Conditional Duration Models," FRU Working Papers 2006/06, University of Copenhagen. Department of Economics. Finance Research Unit. [Downloadable!]
  11. Anthony D. Hall & Nikolaus Hautsch, 2004. "Order Aggressiveness and Order Book Dynamics," FRU Working Papers 2005/04, University of Copenhagen. Department of Economics. Finance Research Unit. [Downloadable!]
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  12. Wing Lon NG, 2004. "Duration and Order Type Clusters," Econometric Society 2004 Australasian Meetings 272, Econometric Society. [Downloadable!]
  13. Fernandes, Marcelo, 2003. "Bounds for the probability distribution function of the linear ACD process," Economics Working Papers (Ensaios Economicos da EPGE) 488, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
    Other versions:
  14. Kulan Ranasinghe & Mervyn J. Silvapulle, 2008. "Semiparametric estimation of duration models when the parameters are subject to inequality constraints and the error distribution is unknown," Monash Econometrics and Business Statistics Working Papers 5/08, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  15. Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," Working Paper Series in Economics and Finance 573, Stockholm School of Economics, revised 20 Apr 2007. [Downloadable!]
    Other versions:
  16. Kulan Ranasinghe & Mervyn J. Silvapulle, 2008. "Semiparametric estimation of duration models when the parameters are subject to inequality constraints and the error distribution is unknown," Monash Econometrics and Business Statistics Working Papers 1/08, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  17. Yongmiao Hong & Yoon-Jin Lee, 2007. "Detecting Misspecifications in Autoregressive Conditional Duration Models," Caepr Working Papers 2007-019, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington. [Downloadable!]
  18. Stanislav Anatolyev, 2006. "Dynamic modeling under linear-exponential loss," Working Papers w0092, Center for Economic and Financial Research (CEFIR). [Downloadable!]
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