IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v13y1967i7p525-557.html
   My bibliography  Save this article

The Analysis of Simulation-Generated Time Series

Author

Listed:
  • George S. Fishman

    (The RAND Corporation)

  • Philip J. Kiviat

    (The RAND Corporation)

Abstract

This study applies spectral analysis to the study of time series data generated by simulated stochastic models. Because these data are autocorrelated, analysis by methods applicable to independent observations is not possible. Mathematical models known as covariance stationary stochastic processes are useful representations of autocorrelated time series. The increased publication of literature describing stochastic processes and spectral analysis, in particular, is making these ideas available to an increasing audience. Section I presents a rationale for our interest in time series models and spectral analysis. Section II describes the basic notions of covariance stationary processes. It emphasizes the equivalence of these processes in both the time and frequency domains; the compactness of frequency domain analysis seemingly recommends it over correlation analysis. Section III provides a heuristic background for understanding statistical spectral analysis. Simple frequency-domain statistical properties are emphasized and compared with the rather involved sampling properties of estimated correlograms. Several relevant statistical tests are described. Three simulated experiments are used as examples of how to apply spectral analysis. These are described in Section IV. They are (1) a single-server, first-come-first-served (FCFS) queueing problem with Poisson arrivals and exponentially distributed service times; (2) a similar model with the FCFS assignment rule replaced by one that chooses the job with the shortest service time; and (3) yet another similar model, but with constant service time. In this third example both assignment rules are equivalent. The state of the queue was observed and recorded at unit intervals for all three examples and forms the time series on which Section V is based; theoretical and statistical correlograms and spectra are compared for example 1; examples 1 and 2 are compared using estimated correlograms and spectra; example 3 serves to show some unusual properties of spectra. A particular conclusion of this paper is that differences in the statistical properties of queue length that result under various assumptions and operating rules are easily identified using spectral analysis. More generally, however, this estimation procedure provides a tool for (1) comparing simulated time series with real-world data, and (2) for understanding the implications that various alternative assumptions have on the output of simulated stochastic models.

Suggested Citation

  • George S. Fishman & Philip J. Kiviat, 1967. "The Analysis of Simulation-Generated Time Series," Management Science, INFORMS, vol. 13(7), pages 525-557, March.
  • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:7:p:525-557
    DOI: 10.1287/mnsc.13.7.525
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.13.7.525
    Download Restriction: no

    File URL: https://libkey.io/10.1287/mnsc.13.7.525?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lada, Emily K. & Wilson, James R., 2006. "A wavelet-based spectral procedure for steady-state simulation analysis," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1769-1801, November.
    2. Pachepsky, L. B. & Haskett, J. D. & Acock, B., 1996. "An adequate model of photosynthesis--I Parameterization, validation and comparison of models," Agricultural Systems, Elsevier, vol. 50(2), pages 209-225.
    3. J Martens & R Peeters & F Put, 2009. "Analysing steady-state simulation output using vector autoregressive processes with exogenous variables," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(5), pages 696-705, May.
    4. Pat-Anthony Federico & Paul W. Figliozzi, 1981. "Computer Simulation of Social Systems," Sociological Methods & Research, , vol. 9(4), pages 513-533, May.
    5. Barry L. Nelson, 2004. "50th Anniversary Article: Stochastic Simulation Research in Management Science," Management Science, INFORMS, vol. 50(7), pages 855-868, July.
    6. Anagnostopoulos, Dimosthenis & Dalakas, Vassilis & Nikolaidou, Mara, 2004. "A m-fold-decimation-based technique for model validation using a single system output data set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(3), pages 273-288.
    7. Duket, Steven D. & Pritsker, A.Alan B., 1978. "Examination of simulation output using spectral methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(1), pages 53-60.
    8. Morgan, Lucy E. & Barton, Russell R., 2022. "Fourier trajectory analysis for system discrimination," European Journal of Operational Research, Elsevier, vol. 296(1), pages 203-217.
    9. Edgar E. Twine & James Rude & Jim Unterschultz, 2016. "Canadian Cattle Cycles and Market Shocks," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 64(1), pages 119-146, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:13:y:1967:i:7:p:525-557. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.