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Copula-Based Multivariate Input Models for Stochastic Simulation


  • Bahar Biller

    () (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)


As large-scale discrete-event stochastic simulation becomes a tool that is used routinely for the design and analysis of stochastic systems, the need for input-modeling support with the ability to represent complex interactions and interdependencies among the components of multivariate time-series input processes is more critical than ever. Motivated by the failure of independent and identically distributed random variables to represent such input processes, a comprehensive framework called Vector-Autoregressive-To-Anything (VARTA) has been introduced for multivariate time-series input modeling. Despite its flexibility in capturing a wide variety of distributional shapes, we show that VARTA falls short in representing dependence structures that arise in situations where extreme component realizations occur together. We demonstrate that it is possible to extend VARTA to work for such dependence structures via the use of the copula theory, which has been used primarily for random vectors in the simulation input-modeling literature, for multivariate time-series input modeling. We show that our copula-based multivariate time-series input model, which includes VARTA as a special case, allows the development of statistically valid fitting and fast sampling algorithms well suited for driving large-scale stochastic simulations.

Suggested Citation

  • Bahar Biller, 2009. "Copula-Based Multivariate Input Models for Stochastic Simulation," Operations Research, INFORMS, vol. 57(4), pages 878-892, August.
  • Handle: RePEc:inm:oropre:v:57:y:2009:i:4:p:878-892

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    References listed on IDEAS

    1. Andrew J. Patton, 2006. "Estimation of multivariate models for time series of possibly different lengths," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 147-173.
    2. Bahar Biller & Barry L. Nelson, 2005. "Fitting Time-Series Input Processes for Simulation," Operations Research, INFORMS, vol. 53(3), pages 549-559, June.
    3. Bahar Biller & Barry L. Nelson, 2008. "Evaluation of the ARTAFIT Method for Fitting Time-Series Input Processes for Simulation," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 485-498, August.
    4. Huifen Chen, 2001. "Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 312-331, November.
    5. Marne C. Cario & Barry L. Nelson, 1998. "Numerical Methods for Fitting and Simulating Autoregressive-to-Anything Processes," INFORMS Journal on Computing, INFORMS, vol. 10(1), pages 72-81, February.
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    Cited by:

    1. Ruben Loaiza-Maya & Michael Stanley Smith, 2017. "Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series," Papers 1712.09150,, revised Jul 2018.
    2. repec:taf:jnlbes:v:34:y:2016:i:3:p:416-434 is not listed on IDEAS
    3. repec:spr:psycho:v:82:y:2017:i:4:d:10.1007_s11336-017-9569-6 is not listed on IDEAS
    4. Tianyang Wang & James S. Dyer, 2012. "A Copulas-Based Approach to Modeling Dependence in Decision Trees," Operations Research, INFORMS, vol. 60(1), pages 225-242, February.
    5. repec:spr:eurjdp:v:5:y:2017:i:1:d:10.1007_s40070-017-0071-2 is not listed on IDEAS
    6. repec:eee:eneeco:v:74:y:2018:i:c:p:886-903 is not listed on IDEAS

    More about this item


    correlation; estimation; sampling; time series;


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