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Fitting Time-Series Input Processes for Simulation

Author

Listed:
  • Bahar Biller

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

  • Barry L. Nelson

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

Providing accurate and automated input-modeling support is one of the challenging problems in the application of computer simulation of stochastic systems. The models incorporated in current input-modeling software packages often fall short because they assume independent and identically distributed processes, even though dependent time-series input processes occur naturally in the simulation of many real-life systems. Therefore, this paper introduces a statistical methodology for fitting stochastic models to dependent time-series input processes. Specifically, an automated and statistically valid algorithm is presented to fit autoregressive-to-anything (ARTA) processes with marginal distributions from the Johnson translation system to stationary univariate time-series data. ARTA processes are particularly well suited to driving stochastic simulations. The use of this algorithm is illustrated with examples.

Suggested Citation

  • Bahar Biller & Barry L. Nelson, 2005. "Fitting Time-Series Input Processes for Simulation," Operations Research, INFORMS, vol. 53(3), pages 549-559, June.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:3:p:549-559
    DOI: 10.1287/opre.1040.0190
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    References listed on IDEAS

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    1. 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. Ng, Chi Tim & Joe, Harry, 2010. "Generating random AR(p) and MA(q) Toeplitz correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1532-1545, July.
    2. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    3. 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.
    4. Bahar Biller, 2009. "Copula-Based Multivariate Input Models for Stochastic Simulation," Operations Research, INFORMS, vol. 57(4), pages 878-892, August.
    5. 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.
    6. Civelek, Ismail & Biller, Bahar & Scheller-Wolf, Alan, 2021. "Impact of dependence on single-server queueing systems," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1031-1045.
    7. Henry Lam, 2018. "Sensitivity to Serial Dependency of Input Processes: A Robust Approach," Management Science, INFORMS, vol. 64(3), pages 1311-1327, March.
    8. He, Miao & Zhao, Lei & Powell, Warren B., 2012. "Approximate dynamic programming algorithms for optimal dosage decisions in controlled ovarian hyperstimulation," European Journal of Operational Research, Elsevier, vol. 222(2), pages 328-340.
    9. Miao He & Lei Zhao & Warren Powell, 2010. "Optimal control of dosage decisions in controlled ovarian hyperstimulation," Annals of Operations Research, Springer, vol. 178(1), pages 223-245, July.
    10. Xuefei Lu & Alessandro Rudi & Emanuele Borgonovo & Lorenzo Rosasco, 2020. "Faster Kriging: Facing High-Dimensional Simulators," Operations Research, INFORMS, vol. 68(1), pages 233-249, January.
    11. Aristidis K. Nikoloulopoulos & Peter G. Moffatt, 2019. "Coupling Couples With Copulas: Analysis Of Assortative Matching On Risk Attitude," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 654-666, January.

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