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The moments of Log-ACD models

Author

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  • BAUWENS, Luc
  • GALLi, Fausto
  • GIOT, Pierre

Abstract

We provide existence conditions and analytical expressions of the moments of logarithmic autoregressive conditional duration (Log-ACD) models. We focus on the dispersion index and the autocorrelation function and compare them with those of ACD (Engle and Russell 1998) and SCD models. Using duration data for several stocks traded on the New York Stock Exchange, we compare the models in terms of their ability at fitting some stylized facts.
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Suggested Citation

  • BAUWENS, Luc & GALLi, Fausto & GIOT, Pierre, 2009. "The moments of Log-ACD models," LIDAM Reprints CORE 2023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2023
    Note: In : Quantitative and Qualitative Analysis in Social Sciences, 2(1), 1-28, 2008
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    References listed on IDEAS

    as
    1. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," LIDAM Discussion Papers CORE 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. David Veredas & Juan Rodriguez-Poo & Antoni Espasa, 2001. "On the (Intradaily) Seasonality and Dynamics of a Financial Point Process : A Semiparametric Approach," Working Papers 2001-19, Center for Research in Economics and Statistics.
    4. 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.
    5. Ghysels, Eric & Gourieroux, Christian & Jasiak, Joann, 2004. "Stochastic volatility duration models," Journal of Econometrics, Elsevier, vol. 119(2), pages 413-433, April.
    6. Luc Bauwens & Pierre Giot, 2000. "The Logarithmic ACD Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks," Annals of Economics and Statistics, GENES, issue 60, pages 117-149.
    7. repec:adr:anecst:y:2000:i:60:p:05 is not listed on IDEAS
    8. Joachim Grammig & Kai-Oliver Maurer, 2000. "Non-monotonic hazard functions and the autoregressive conditional duration model," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 16-38.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Xuehai Zhang, 2019. "A Box-Cox semiparametric multiplicative error model," Working Papers CIE 122, Paderborn University, CIE Center for International Economics.
    2. Xiufeng Yan, 2021. "Autoregressive conditional duration modelling of high frequency data," Papers 2111.02300, arXiv.org.
    3. Katarzyna Bień-Barkowska, 2011. "Multistate asymmetric ACD model: an application to order dynamics in the EUR/PLN spot market," NBP Working Papers 104, Narodowy Bank Polski.
    4. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    5. Fabrizio Cipollini & Giampiero M Gallo & Alessandro Palandri, 2020. "Realized Variance Modeling: Decoupling Forecasting from Estimation," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 532-555.
    6. Helton Saulo & Narayanaswamy Balakrishnan & Roberto Vila, 2021. "On a quantile autoregressive conditional duration model applied to high-frequency financial data," Papers 2109.03844, arXiv.org.
    7. Wing Lon NG, 2004. "Duration and Order Type Clusters," Econometric Society 2004 Far Eastern Meetings 730, Econometric Society.
    8. Feng, Yuanhua & Zhou, Chen, 2015. "Forecasting financial market activity using a semiparametric fractionally integrated Log-ACD," International Journal of Forecasting, Elsevier, vol. 31(2), pages 349-363.
    9. Ola Simonsen, 2007. "An empirical model for durations in stocks," Annals of Finance, Springer, vol. 3(2), pages 241-255, March.
    10. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 89-121.
    11. Hautsch, Nikolaus, 2008. "Capturing common components in high-frequency financial time series: A multivariate stochastic multiplicative error model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3978-4015, December.
    12. Allen, David & Chan, Felix & McAleer, Michael & Peiris, Shelton, 2008. "Finite sample properties of the QMLE for the Log-ACD model: Application to Australian stocks," Journal of Econometrics, Elsevier, vol. 147(1), pages 163-185, November.
    13. Yuanhua Feng & Jan Beran & Sebastian Letmathe & Sucharita Ghosh, 2020. "Fractionally integrated Log-GARCH with application to value at risk and expected shortfall," Working Papers CIE 137, Paderborn University, CIE Center for International Economics.
    14. Simonsen, Ola, 2006. "The Impact of News Releases on Trade Durations in Stocks -Empirical Evidence from Sweden," Umeå Economic Studies 688, Umeå University, Department of Economics.
    15. Aerambamoorthy Thavaneswaran & Nalini Ravishanker & You Liang, 2015. "Generalized duration models and optimal estimation using estimating functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 129-156, February.
    16. Jan Beran & Yuanhua Feng & Sucharita Ghosh, 2015. "Modelling long-range dependence and trends in duration series: an approach based on EFARIMA and ESEMIFAR models," Statistical Papers, Springer, vol. 56(2), pages 431-451, May.
    17. Simonsen, Ola, 2006. "Stock Data, Trade Durations, And Limit Order Book Information," Umeå Economic Studies 689, Umeå University, Department of Economics.
    18. Xuehai Zhang, 2019. "A Box-Cox semiparametric multiplicative error model," Working Papers CIE 125, Paderborn University, CIE Center for International Economics.
    19. Wing Lon NG, 2004. "Duration and Order Type Clusters," Econometric Society 2004 Australasian Meetings 272, Econometric Society.
    20. Simonsen, Ola, 2005. "An Empirical Model for Durations in Stocks," Umeå Economic Studies 657, Umeå University, Department of Economics.

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    More about this item

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies

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