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Bayesian Inference of Asymmetric Stochastic Conditional Duration Models

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Author Info

  • Zhongxian Men

    (Department of Statistics & Actuarial Science, University of Waterloo, Canada)

  • Adam W. Kolkiewicz

    (Department of Statistics & Actuarial Science, University of Waterloo, Canada)

  • Tony S. Wirjanto

    ()
    (Department of Statistics & Actuarial Science, University of Waterloo, Canada)

Abstract

This paper extends stochastic conditional duration (SCD) models for financial transaction data to allow for correlation between error processes or innovations of observed duration process and latent log duration process. Novel algorithms of Markov Chain Monte Carlo (MCMC) are developed to fit the resulting SCD models under various distributional assumptions about the innovation of the measurement equation. Unlike the estimation methods commonly used to estimate the SCD models in the literature, we work with the original specification of the model, without subjecting the observation equation to a logarithmic transformation. Results of simulation studies suggest that our proposed models and corresponding estimation methodology perform quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample duration forecasts of the fitted models. Applications to the IBM transaction data allows comparison of our models and methods to those existing in the literature.

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Bibliographic Info

Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 28_13.

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Date of creation: May 2013
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Handle: RePEc:rim:rimwps:28_13

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Related research

Keywords: Stochastic Duration; Bayesian Inference; Markov Chain Monte Carlo; Leverage Effect; Acceptance-rejection; Slice Sampler;

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References

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  1. Bauwens, L. & Lubrano, M., . "Bayesian inference on GARCH models using the Gibbs sampler," CORE Discussion Papers RP -1307, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Dinghai Xu & John Knight & Tony S. Wirjanto, 2011. "Asymmetric Stochastic Conditional Duration Model--A Mixture-of-Normal Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(3), pages 469-488, Summer.
  3. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer, vol. 52(3), pages 317-332, September.
  4. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
  5. Neil Shephard & Siddhartha Chib, 1999. "Analysis of High Dimensional Multivariate Stochastic Volatility Models," Economics Series Working Papers 1999-W18, University of Oxford, Department of Economics.
  6. Berg, Andreas & Meyer, Renate & Yu, Jun, 2004. "Deviance Information Criterion for Comparing Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 107-20, January.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
  9. Xibin Zhang & Maxwell L. King, 2004. "Box-Cox Stochastic Volatility Models with Heavy-Tails and Correlated Errors," Monash Econometrics and Business Statistics Working Papers 26/04, Monash University, Department of Econometrics and Business Statistics.
  10. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
  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.
  12. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  13. BAUWENS, Luc & GALLI, Fausto, 2007. "Efficient importance sampling for ML estimation of SCD models," CORE Discussion Papers 2007053, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Working Papers 13-2004, Singapore Management University, School of Economics.
  15. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
  16. John Knight & Cathy Q. Ning, 2008. "Estimation of the stochastic conditional duration model via alternative methods," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 593-616, November.
  17. Gareth O. Roberts & Jeffrey S. Rosenthal, 1999. "Convergence of Slice Sampler Markov Chains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 643-660.
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