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Estimating and simulating Weibull models of risk or price durations: An application to ACD models

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  • Allen, David
  • Ng, K.H.
  • Peiris, Shelton

Abstract

There is now a massive literature on both the GARCH family of risk models and the related Auto-Conditional Duration (ACD) models used for modeling the stochastic timing of trades or price changes in finance market microstructure research. Both have their origins in Engle (1982) and Bollerslev (1986). This paper uses the theory of estimating functions (EF) as a semi-parametric method for estimating the parameters of this type of model. As an example, we consider the class of ACD models with errors from the standard Weibull distribution to develop an estimation procedure. This method could equally be applied to GARCH models. Using a simulation study, it is shown that the EF approach is easier to use in practice than the maximum likelihood (ML) or quasi maximum likelihood (QML) methods. The statistical properties of the corresponding optimal estimates are investigated and it is shown that the estimates using both the EF and QML methods are comparable. However, the EF estimates are easier to evaluate than the ML and QML methods. Nevertheless, ML based estimates are superior and perform better when the true distribution is known, when this is not so EF estimates are a powerful tool.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecofin:v:25:y:2013:i:c:p:214-225
    DOI: 10.1016/j.najef.2012.06.013
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    2. Hammoudeh, Shawkat & McAleer, Michael, 2013. "Risk management and financial derivatives: An overview," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 109-115.
    3. 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.
    4. 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.
    5. Pooi AH-HIN & Ng KOK-HAUR & Soo HUEI-CHING, 2016. "Modelling and Forecasting with Financial Duration Data Using Non-linear Model," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(2), pages 79-92.
    6. Jacobi, Arie & Tzur, Joseph, 2021. "Wealth Distribution across Countries: Quality of Weibull, Dagum and Burr XII in Estimating Wealth over Time," Finance Research Letters, Elsevier, vol. 43(C).
    7. Ng, Kok Haur & Peiris, Shelton & Chan, Jennifer So-kuen & Allen, David & Ng, Kooi Huat, 2017. "Efficient modelling and forecasting with range based volatility models and its application," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 448-460.
    8. Allen, David & Ng, K.H. & Peiris, Shelton, 2013. "The efficient modelling of high frequency transaction data: A new application of estimating functions in financial economics," Economics Letters, Elsevier, vol. 120(1), pages 117-122.

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