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Finite sample properties of the QMLE for the Log-ACD model: Application to Australian stocks

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Author Info

  • Allen, David
  • Chan, Felix
  • McAleer, Michael
  • Peiris, Shelton

Abstract

This paper concerns the properties of the Quasi Maximum Likelihood Estimator (QMLE) of the Logarithmic Autoregressive Conditional Duration (Log-ACD) model. Proofs of consistency and asymptotic normality of QMLE for the Log-ACD model with log-normal density are presented. This is an important issue as the Log-ACD is used widely for testing various market microstructure models and effects. Knowledge of the distribution of the QMLE is crucial for purposes of valid inference and diagnostic checking. The theoretical results developed in the paper are evaluated using Monte Carlo experiments. The experimental results also provide insights into the finite sample properties of the Log-ACD model under different distributional assumptions. Finally, this paper presents two extensions to the Log-ACD model to accommodate asymmetric effects. The usefulness of these novel models will be evaluated empirically using data from Australian stocks.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 147 (2008)
Issue (Month): 1 (November)
Pages: 163-185

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Handle: RePEc:eee:econom:v:147:y:2008:i:1:p:163-185

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Conditional duration Asymmetry ACD Log-ACD Monte Carlo simulation;

References

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  1. BAUWENS, Luc & GALLi, Fausto & GIOT, Pierre, . "The moments of Log-ACD models," CORE Discussion Papers RP -2023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  8. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
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  11. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
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  14. 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, Elsevier, vol. 104(1), pages 179-207, August.
  15. Russell, Jeffrey R. & Engle, Robert F., 2005. "A Discrete-State Continuous-Time Model of Financial Transactions Prices and Times: The Autoregressive Conditional Multinomial-Autoregressive Conditional Duration Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 23, pages 166-180, April.
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Citations

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Cited by:
  1. Hautsch, Nikolaus & Malec, Peter & Schienle, Melanie, 2011. "Capturing the zero: A new class of zero-augmented distributions and multiplicative error processes," CFS Working Paper Series 2011/25, Center for Financial Studies (CFS).
  2. 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.
  3. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, Elsevier, vol. 177(1), pages 34-46.
  4. repec:ecu:wpaper:2009-01 is not listed on IDEAS
  5. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, Elsevier, vol. 80(10), pages 2062-2078.

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