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

Listed author(s):
  • Allen, David
  • Ng, K.H.
  • Peiris, Shelton

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.

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File URL: http://www.sciencedirect.com/science/article/pii/S1062940812000642
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Article provided by Elsevier in its journal The North American Journal of Economics and Finance.

Volume (Year): 25 (2013)
Issue (Month): C ()
Pages: 214-225

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Handle: RePEc:eee:ecofin:v:25:y:2013:i:c:p:214-225
DOI: 10.1016/j.najef.2012.06.013
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/620163

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  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
  2. Grammig, Joachim & Wellner, Marc, 2002. "Modeling the interdependence of volatility and inter-transaction duration processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 369-400, February.
  3. Li, David X & Turtle, H J, 2000. "Semiparametric ARCH Models: An Estimating Function Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 174-186, April.
  4. Bera, Anil K. & Bilias, Yannis, 2002. "The MM, ME, ML, EL, EF and GMM approaches to estimation: a synthesis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 51-86, March.
  5. repec:adr:anecst:y:2000:i:60:p:05 is not listed on IDEAS
  6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  7. Thavaneswaran, A. & Peiris, Shelton, 1996. "Nonparametric estimation for some nonlinear models," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 227-233, July.
  8. Allen, David & Lazarov, Zdravetz & McAleer, Michael & Peiris, Shelton, 2009. "Comparison of alternative ACD models via density and interval forecasts: Evidence from the Australian stock market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2535-2555.
  9. 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.
  10. 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.
  11. 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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