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On a quantile autoregressive conditional duration model

Author

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  • Saulo, Helton
  • Balakrishnan, Narayanaswamy
  • Vila, Roberto

Abstract

Autoregressive conditional duration (ACD) models are primarily used to deal with data arising from times between two successive events. These models are usually specified in terms of a time-varying conditional mean or median duration. In this work, we relax this assumption and consider a conditional quantile approach to facilitate the modeling of different percentiles. The proposed ACD quantile model is based on a skewed version of Birnbaum–Saunders distribution, which yields better fit of the tails than the traditional Birnbaum–Saunders distribution, in addition to facilitating the implementation of an expectation conditional maximization (ECM) algorithm. A Monte Carlo simulation study is performed to assess the behavior of the model as well as the parameter estimation method and the evaluation of a form of residuals. Two real financial transaction data sets are finally analyzed to illustrate the proposed approach.

Suggested Citation

  • Saulo, Helton & Balakrishnan, Narayanaswamy & Vila, Roberto, 2023. "On a quantile autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 425-448.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:425-448
    DOI: 10.1016/j.matcom.2022.06.032
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    References listed on IDEAS

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    1. Saranjeet Kaur Bhogal & Ramanathan Thekke Variyam, 2019. "Conditional Duration Models For High‐Frequency Data: A Review On Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 33(1), pages 252-273, February.
    2. De Luca, Giovanni & Zuccolotto, Paola, 2006. "Regime-switching Pareto distributions for ACD models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2179-2191, December.
    3. 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, September.
    4. 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.
    5. repec:adr:anecst:y:2000:i:60:p:05 is not listed on IDEAS
    6. 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.
    7. Luc Bauwens & Pierre Giot, 2003. "Asymmetric ACD models: Introducing price information in ACD models," Empirical Economics, Springer, vol. 28(4), pages 709-731, November.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Helton Saulo & Jeremias Leão, 2017. "On log-symmetric duration models applied to high frequency financial data," Economics Bulletin, AccessEcon, vol. 37(2), pages 1089-1097.
    10. 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.
    11. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    12. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2021. "Birnbaum‐Saunders quantile regression and its diagnostics with application to economic data," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 37(1), pages 53-73, January.
    13. Helton Saulo & Jeremias Leão & Víctor Leiva & Robert G. Aykroyd, 2019. "Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data," Statistical Papers, Springer, vol. 60(5), pages 1605-1629, October.
    14. 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.
    15. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    16. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
    17. Danúbia R. Cunha & Roberto Vila & Helton Saulo & Rodrigo N. Fernandez, 2020. "A General Family of Autoregressive Conditional Duration Models Applied to High-Frequency Financial Data," JRFM, MDPI, vol. 13(3), pages 1-20, March.
    18. Vilca, Filidor & Santana, Lucia & Leiva, Víctor & Balakrishnan, N., 2011. "Estimation of extreme percentiles in Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1665-1678, April.
    19. N. Balakrishnan & Debasis Kundu, 2019. "Birnbaum‐Saunders distribution: A review of models, analysis, and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(1), pages 4-49, January.
    20. Yiu-kuen Tse & Thomas Tao Yang, 2012. "Estimation of High-Frequency Volatility: An Autoregressive Conditional Duration Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 533-545, April.
    21. 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.
    22. Allen, David & Ng, K.H. & Peiris, Shelton, 2013. "Estimating and simulating Weibull models of risk or price durations: An application to ACD models," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 214-225.
    23. Chiang Min-Hsien, 2007. "A Smooth Transition Autoregressive Conditional Duration Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(1), pages 108-144, March.
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