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Confidence intervals in stationary autocorrelated time series

  • Halkos, George
  • Kevork, Ilias

In this study we examine in covariance stationary time series the consequences of constructing confidence intervals for the population mean using the classical methodology based on the hypothesis of independence. As criteria we use the actual probability the confidence interval of the classical methodology to include the population mean (actual confidence level), and the ratio of the sampling error of the classical methodology over the corresponding actual one leading to equality between actual and nominal confidence levels. These criteria are computed analytically under different sample sizes, and for different autocorrelation structures. For the AR(1) case, we find significant differentiation in the values taken by the two criteria depending upon the structure and the degree of autocorrelation. In the case of MA(1), and especially for positive autocorrelation, we always find actual confidence levels lower than the corresponding nominal ones, while this differentiation between these two levels is much lower compared to the case of AR(1).

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 31840.

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Date of creation: 2002
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Handle: RePEc:pra:mprapa:31840
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  1. George S. Fishman, 1971. "Estimating Sample Size in Computing Simulation Experiments," Management Science, INFORMS, vol. 18(1), pages 21-38, September.
  2. Averill M. Law & W. David Kelton, 1982. "Confidence Intervals for Steady-State Simulations II: A Survey of Sequential Procedures," Management Science, INFORMS, vol. 28(5), pages 550-562, May.
  3. R. W. Conway, 1963. "Some Tactical Problems in Digital Simulation," Management Science, INFORMS, vol. 10(1), pages 47-61, October.
  4. Park, Dae S. & Kim, Yun B. & Shin, Key I. & Willemain, Thomas R., 2001. "Simulation output analysis using the threshold bootstrap," European Journal of Operational Research, Elsevier, vol. 134(1), pages 17-28, October.
  5. Song, Wheyming Tina, 1996. "On the estimation of optimal batch sizes in the analysis of simulation output," European Journal of Operational Research, Elsevier, vol. 88(2), pages 304-319, January.
  6. Wheyming Tina Song & Bruce W. Schmeiser, 1995. "Optimal Mean-Squared-Error Batch Sizes," Management Science, INFORMS, vol. 41(1), pages 110-123, January.
  7. Michael A. Crane & Donald L. Iglehart, 1975. "Simulating Stable Stochastic Systems, IV: Approximation Techniques," Management Science, INFORMS, vol. 21(11), pages 1215-1224, July.
  8. 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.
  9. Park, Daesu & Willemain, Thomas R., 1999. "The threshold bootstrap and threshold jackknife," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 187-202, August.
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