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Διαστήματα Εμπιστοσύνης Για Εκατοστημόρια Σε Στάσιμες Arma Διαδικασίες: Μία Εμπειρική Εφαρμογή Σε Περιβαλλοντικά Δεδομένα
[Confidence intervals for percentiles in stationary ARMA processes: An application using environmental data]

Author

Listed:
  • Halkos, George
  • Kevork, Ilias

Abstract

Percentiles estimation plays an important role at the stage of making decisions in many scientific fields. However, the up-to-now research on developing estimation methods for percentiles has been based on the assumption that the data in the sample are formed independently. In the current paper we suppress this restrictive assumption by assuming that the values of the variable under study are formed according to the general linear process. After deriving the asymptotic distribution of the Maximum Likelihood estimator for the 100×Pth percentile, we give the general form of the corresponding asymptotic confidence interval. Then, the performance of the estimated asymptotic confidence interval is evaluated in finite samples from the stationary AR(1) and ARMA(1,1) through Monte-Carlo simulations by computing two statistical criteria: (a) the actual confidence level, (b) the expected half-length as percentage of the true value of the percentile. Simulation results show that the validity of the estimated asymptotic confidence interval depends upon the sample size, the size of the 1st order theoretical autocorrelation coefficient, and the true cumulative probability P related to the percentile. Finally, an application example is given using the series of the CO2 annual emissions intensity in Greece (kg per kg of oil equivalent energy use) for the period 1961-2010. Confidence intervals for percentiles are constructed on this series and discussion about the validity of the estimation procedure follows according to the findings from the simulation experiments regarding the values of the aforementioned criteria.

Suggested Citation

  • Halkos, George & Kevork, Ilias, 2014. "Διαστήματα Εμπιστοσύνης Για Εκατοστημόρια Σε Στάσιμες Arma Διαδικασίες: Μία Εμπειρική Εφαρμογή Σε Περιβαλλοντικά Δεδομένα [Confidence intervals for percentiles in stationary ARMA processes: An appl," MPRA Paper 56134, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:56134
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    References listed on IDEAS

    as
    1. J. Keating & R. Mason & N. Balakrishnan, 2010. "Percentile estimators in location-scale parameter families under absolute loss," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 351-367, November.
    2. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand," MPRA Paper 39650, University Library of Munich, Germany.
    3. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, vol. 38(3-4), pages 218-227, June.
    4. Chakraborti, S. & Li, J., 2007. "Confidence Interval Estimation of a Normal Percentile," The American Statistician, American Statistical Association, vol. 61, pages 331-336, November.
    5. Halkos, George & Kevork, Ilias, 2013. "Forecasting the optimal order quantity in the newsvendor model under a correlated demand," MPRA Paper 44189, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Percentiles; environmental data; time series models; confidence intervals.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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