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H Ασυμπτωτική Διακύμανση Στην Εκτίμηση Του Στάσιμου Μέσου Υπό Συνθήκες Αυτοσυσχέτισης
[Using the asymptotic variance to estimate the stationary mean under autocorrelation]

Author

Listed:
  • George, Halkos
  • Ilias, Kevork

Abstract

In this study, using Monte Carlo simulations, we evaluate three alternative methods for constructing confidence intervals for the population mean in the case of a stationary first order autoregressive process, AR(1), with parameter ф. Differentiating the three methodologies with respect to the way of estimating the asymptotic variance, we infer that in constructing confidence intervals we have to avoid the use of the observations of the time series under consideration for the estimation of the autovariance and the autocorrelation coefficients. Instead, it is preferable to identify the series according to Box-Jenkins and then use the asymptotic variance derived from the corresponding ARMA model after the substitution of the OLS parameter and error variance estimates. It is worth mentioning that using the asymptotic variance, for small samples and in the case of an AR(1) with positive ф values, the expected actual confidence levels are larger as compared to the corresponding nominal ones, indicating a potential area for future research.

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:33324
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    References listed on IDEAS

    as
    1. Michael A. Crane & Donald L. Iglehart, 1975. "Simulating Stable Stochastic Systems, IV: Approximation Techniques," Management Science, INFORMS, vol. 21(11), pages 1215-1224, July.
    2. George Halkos & Ilias Kevork, 2005. "A comparison of alternative unit root tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(1), pages 45-60.
    3. Halkos, George & Kevork, Ilias, 2002. "Confidence intervals in stationary autocorrelated time series," MPRA Paper 31840, University Library of Munich, Germany.
    4. 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.
    5. Wheyming Tina Song & Bruce W. Schmeiser, 1995. "Optimal Mean-Squared-Error Batch Sizes," Management Science, INFORMS, vol. 41(1), pages 110-123, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Ασυμπτωτική διακύμανση δειγματικού μέσου; διαστήματα εμπιστοσύνης; αυτοπαλίνδρομο σχήμα πρώτου βαθμού AR(1);
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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