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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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:147:y:2008:i:1:p:163-185
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Bhatti, Chad R., 2009. "On the interday homogeneity in the intraday rate of trading," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2250-2257.
    2. Bhatti, Chad R., 2009. "Intraday trade and quote dynamics: A Cox regression analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2240-2249.
    3. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, vol. 177(1), pages 34-46.
    4. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    5. Feng, Yuanhua & Zhou, Chen, 2015. "Forecasting financial market activity using a semiparametric fractionally integrated Log-ACD," International Journal of Forecasting, Elsevier, vol. 31(2), pages 349-363.
    6. Vasileios Siakoulis & Ioannis Venetis, 2015. "On inter-arrival times of bond market extreme events. An application to seven European markets," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 39(4), pages 717-741, October.
    7. Maurice Peat, 2009. "Market Data Resources for Researchers: The SIRCA Data Repository," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 42(4), pages 490-495.
    8. Perera, Indeewara & Koul, Hira L., 2017. "Fitting a two phase threshold multiplicative error model," Journal of Econometrics, Elsevier, vol. 197(2), pages 348-367.
    9. 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.
    10. Siakoulis, Vasilios, 2015. "Modeling bank default intensity in the USA using autoregressive duration models," MPRA Paper 64526, University Library of Munich, Germany.
    11. Roman Huptas, 2014. "Bayesian Estimation and Prediction for ACD Models in the Analysis of Trade Durations from the Polish Stock Market," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 6(4), pages 237-273, December.
    12. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    13. 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.
    14. Aerambamoorthy Thavaneswaran & Nalini Ravishanker & You Liang, 2015. "Generalized duration models and optimal estimation using estimating functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 129-156, February.
    15. Richard Gerlach & Shelton Peiris & Edward M. H. Lin, 2016. "Bayesian estimation and inference for log-ACD models," Computational Statistics, Springer, vol. 31(1), pages 25-48, March.
    16. Roman Huptas, 2016. "The UHF-GARCH-Type Model in the Analysis of Intraday Volatility and Price Durations – the Bayesian Approach," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 8(1), pages 1-20, March.
    17. Min-Hsien Chiang & Ray Yeutien Chou & Li-Min Wang, 2016. "Outlier Detection in the Lognormal Logarithmic Conditional Autoregressive Range Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(1), pages 126-144, February.

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