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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).

Suggested Citation

  • Halkos, George & Kevork, Ilias, 2002. "Confidence intervals in stationary autocorrelated time series," MPRA Paper 31840, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:31840

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    References listed on IDEAS

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    3. 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.
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    5. R. W. Conway, 1963. "Some Tactical Problems in Digital Simulation," Management Science, INFORMS, vol. 10(1), pages 47-61, October.
    6. 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.
    7. N/A, 1984. "Confidence Intervals," National Institute Economic Review, National Institute of Economic and Social Research, vol. 109(1), pages 33-37, August.
    8. George S. Fishman, 1971. "Estimating Sample Size in Computing Simulation Experiments," Management Science, INFORMS, vol. 18(1), pages 21-38, September.
    9. 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.
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    Cited by:

    1. George, Halkos & Ilias, Kevork, 2004. "H Ασυμπτωτική Διακύμανση Στην Εκτίμηση Του Στάσιμου Μέσου Υπό Συνθήκες Αυτοσυσχέτισης
      [Using the asymptotic variance to estimate the stationary mean under autocorrelation]
      ," MPRA Paper 33324, University Library of Munich, Germany.

    More about this item


    Covariance stationary time series; Variance of the sample mean; Actual confidence level;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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