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

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  • 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. Alfonso Dufour & Robert F. Engle, 2000. "Time and the Price Impact of a Trade," Journal of Finance, American Finance Association, vol. 55(6), pages 2467-2498, December.
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  3. 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, vol. 23, pages 166-180, April.
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  5. Meitz, Mika & Teräsvirta, Timo, 2004. "Evaluating models of autoregressive conditional duration," Working Paper Series in Economics and Finance 557, Stockholm School of Economics, revised 13 Dec 2004.
  6. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  7. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
  8. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
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  10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  11. Robert F. Engle & Jeffrey R. Russell, 1994. "Forecasting Transaction Rates: The Autoregressive Conditional Duration Model," NBER Working Papers 4966, National Bureau of Economic Research, Inc.
  12. 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.
  13. Nikolaus Hautsch, 2006. "Testing the Conditional Mean Function of Autoregressive Conditional Duration Models," FRU Working Papers 2006/06, University of Copenhagen. Department of Economics. Finance Research Unit.
  14. 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).
  15. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  16. 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.
  17. Engle, Robert F. & Russell, Jeffrey R., 1997. "Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 187-212, June.
  18. Barclay, Michael J. & Warner, Jerold B., 1993. "Stealth trading and volatility : Which trades move prices?," Journal of Financial Economics, Elsevier, vol. 34(3), pages 281-305, December.
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Citations

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Cited by:
  1. Hautsch, Nikolaus & Malec, Peter & Schienle, Melanie, 2010. "Capturing the zero: A new class of zero-augmented distributions and multiplicative error processes," CFS Working Paper Series 2010/19, 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 & Zakoian, Jean-Michel, 2012. "Garch models without positivity constraints: exponential or log garch?," MPRA Paper 41373, University Library of Munich, Germany.
  4. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
  5. repec:ecu:wpaper:2009-01 is not listed on IDEAS

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