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Bayesian Inference of Multiscale Stochastic Conditional Duration Models

Author

Listed:
  • Zhongxian Men

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

  • Tony S. Wirjanto

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

  • Adam W. Kolkiewicz

    (Department of Statistics and Actuarial Science, School of Accounting and Finance, University of Waterloo, Canada)

Abstract

There is evidence to suggest that a single factor of duration running on single time scale is not adequate to capture the dynamics of the duration process of financial transaction data. This assertion is motivated by the observation that some existing one-factor stochastic duration models have had difficulty in successfully fitting the left tail of the marginal distribution of the observed durations. This empirical poor fit of the left tail of the duration distribution may be indicative of the possible existence of multiple stochastic duration factors running on different time scales. This paper proposes multiscale stochastic conditional duration (MSCD) models to describe the dynamics of financial transaction data. Novel algorithms of Markov Chain Monte Carlo (MCMC) are developed to fit the resulting MSCD models under three distributional assumptions about the innovation of the measurement equation. In addition, instead of subjecting the observation equation to a logarithmic transformation, we work on the MSCD model directly. Simulation studies suggest that our proposed models and corresponding estimation methodology work quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample duration forecasts based on the fitted models. Applications to two duration data sets of FIAT and IBM indicate the existence of at least two factors that determine the dynamics of the two stock transactions.

Suggested Citation

  • Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2013. "Bayesian Inference of Multiscale Stochastic Conditional Duration Models," Working Paper series 63_13, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:63_13
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    References listed on IDEAS

    as
    1. 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.
    2. Tony S. Wirjanto & Adam W. Kolkiewicz & Zhongxian Men, 2013. "Stochastic Conditional Duration Models with Mixture Processes," Working Paper series 29_13, Rimini Centre for Economic Analysis.
    3. De Luca Giovanni & Gallo Giampiero M., 2004. "Mixture Processes for Financial Intradaily Durations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-20, May.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2013. "A Threshold Stochastic Conditional Duration Model for Financial Transaction Data," Working Paper series 30_13, Rimini Centre for Economic Analysis.
    6. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 23-46.
    7. Bauwens, L. & Galli, F., 2009. "Efficient importance sampling for ML estimation of SCD models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1974-1992, April.
    8. 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.
    9. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    10. 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 863-883, November.
    11. Hirotugu Akaike, 1987. "Factor analysis and AIC," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 317-332, September.
    12. 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.
    13. Dingan Feng, 2004. "Stochastic Conditional Duration Models with "Leverage Effect" for Financial Transaction Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(3), pages 390-421.
    14. 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 107-120, January.
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    More about this item

    Keywords

    Stochastic conditional Duration; Markov Chain Monte Carlo; Multiscale; Auxiliary particle filter; Probability integral transform; Deviance information criterion;

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