Generation of Simulation input Stream using Threshold Bootstrap

임계값 부트스트랩을 사용한 시뮬레이션 입력 시나리오의 생성

  • 김윤배 (성균관대학교 시스템경영공학부) ;
  • 김재범 (성균관대학교 시스템경영공학부)
  • Published : 2005.05.01

Abstract

The bootstrap is a method of computational inference that simulates the creation of new data by resampling from a single data set. We propose a new job for the bootstrap: generating inputs from one historical trace using Threshold Bootstrap. In this regard, the most important quality of bootstrap samples is that they be functionally indistinguishable from independent samples of the same stochastic process. We describe a quantitative measure of difference between two time series, and demonstrate the sensitivity of this measure for discriminating between two data generating processes. Utilizing this distance measure for the task of generating inputs, we show a way of tuning the bootstrap using a single observed trace. This application of the threshold bootstrap will be a powerful tool for Monte Carlo simulation. Monte Carlo simulation analysis relies on built-in input generators. These generators make unrealistic assumptions about independence and marginal distributions. The alternative source of inputs, historical trace data, though realistic by definition, provides only a single input stream for simulation. One benefit of our method would be expanding the number of inputs achieving reality by driving system models with actual historical input series. Another benefit might be the automatic generation of lifelike scenarios for the field of finance.

Keywords

References

  1. Bickel, P. and D. Freedman, 'Some Asymptotic Theory for the Bootstrap,' Annals of Statistics, Vol.9(1981), pp.1196-1217 https://doi.org/10.1214/aos/1176345637
  2. Carson, J.S., 'Convincing User's of Model's Validity is Challenging Aspect of Modeler's Job,' Industrial Engineering, Vol.18(1986), pp.74-85
  3. Efron, B., 'Bootstrap Methods : Another Look at the Jackknife,' Annals of Statistics, Vol.7(1979), pp.1-26 https://doi.org/10.1214/aos/1176344552
  4. Efron, B. and R. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall Inc., New York, 1993
  5. Gotze, F. and H.R. Kunsch, Blockwise Bootstrap for Dependent Observation : Higher Order Approximations for Studen-tized Statistics, Technical Report, Univ. Bielefeld, Germany, 1993
  6. Hall, P., J.L. Horowitz and B. Jing, 'On Blocking Rules for the Bootstrap with Dependent Data,' Biometrika, Vol.82(1995), pp.561-74 https://doi.org/10.1093/biomet/82.3.561
  7. Hall, P. and B. Jing, 'On Sample Reuse Methods for Dependent Data,' Journal of the Royal Statistical Society B, Vol.58(1996), pp.727-737
  8. Kim, Y., J. Haddock and T.R. Willemain, 'The Binary Bootstrap : Inference with Autocorrelated Binary Data,' Communications in Statistics : Simulation and Computation, Vol.22(1993a), pp.205-216 https://doi.org/10.1080/03610919308813089
  9. Kim, Y., D.S. Park, K.I. Shin and Willemain, 'Simulation Output Analysis Using the Threshold Bootstrap,' European Journal of Operational Research, Vol.134(2001), pp.17-28 https://doi.org/10.1016/S0377-2217(00)00209-5
  10. Kim, Y., T.R. Willemain, J. Haddock and G. Runger, 'The Threshold Bootstrap : A New Approach to Simulation Output Analysis,' In Proceedings of the 1993 Winter Simulation Conference, G. Evans, M. Mol-laghasemi, E. Russell and W. Biles, eds. IEEE Press : Piscataway, NJ. (1993c), pp. 498-502
  11. Kunsch, H., 'The Jackknife and the Bootstrap for General Stationary Observations,' Annals of Statistics, Vol.17(1989), pp.1217-1241 https://doi.org/10.1214/aos/1176347265
  12. Leemis, L., 'Input Modeling for Discrete Event Simulation,' In Proceedings of the 1995 Winter Simulation Conference, C. Alexopoulos, K. Kang, W. Lilegdon and D. Goldsman, eds. IEEE Press : Piscataway, NJ. (1995) pp.16-23
  13. Liu, R. and K. Singh, 'Moving Blocks Jackknife and Bootstrap Capture Weak Dependence,' In Exploring the Limits of Bootstrap, R. LePage and L. Billard, eds. Wiley : New York, 1992
  14. Melamed, B., J.R. Hill and D. Goldsman, 'The TES Methodology : Modeling Empirical Stationary Time Series,' In Proceedings of the 1992 Winter Simulation Conference, J.J. Swain, D. Goldsman, RC. Crain, and J.R. Wilson, eds. Piscataway, NJ: IEEE Press, (1992), pp.16-23
  15. Omer, F.D. and T.R. Willemain, 'Generation of simulation input scenario using bootstrap methods,' Journal of Operational Research Society, Vol.53(2002), pp.69-78 https://doi.org/10.1057/palgrave/jors/2601251
  16. Omer, F.D. and T.R. Willemain, 'Applications of the Bootstrap in Scenario Generation,' unpublished Ph.D dissertation, Relsselaer Polytechnic Institute, 2001
  17. Park, D., 'The Threshold Bootstrap For Time Series Analysis,' Unpublished Ph.D. Dissertation, Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, 1997
  18. Park, D. and T.R. Willemain, 'The Threshold Bootstrap and Threshold Jackknife,' Computational Statistics and Data Analysis, 1999
  19. Politis, D.N. and J.P. Romano, 'The Stationary Bootstrap,' Journal of the American Statistical Association, Vol.89(1994), pp.1303-1313 https://doi.org/10.2307/2290993
  20. Schruben, L.W., 'Establishing the Credibility of Simulations,' Simulation, Vol.34 (1980), pp.101-1 https://doi.org/10.1177/003754978003400310
  21. Singh, K., 'On The Asymptotic Accuracy of Efron's Bootstrap,' Amm. Statist., Vol.9 (1981), pp.1187-1195 https://doi.org/10.1214/aos/1176345636
  22. Turing, A.M., 'Computing. Machinery and Intelligence,' Mind, Vol.59(1950), pp.433-460