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An Autoregressive Process for Beta Random Variables

Author

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  • Ed McKenzie

    (Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, Scotland and Department of Operations Research, Naval Postgraduate School, Monterey, California 93943)

Abstract

Two stationary first-order autoregressive processes with Beta marginal distributions are presented. They are both linear, additive processes but the coefficients are Beta random variables. Their autocorrelation functions are investigated: one is positive and the other alternates in sign. The usefulness of the models in simulation is discussed. The Bivariate Beta distributions of two consecutive observations are considered in some detail. Several examples are given, including a Bivariate Uniform process which is also examined in detail. The relationship of these Bivariate Beta distributions to the Dirichlet distribution is discussed.

Suggested Citation

  • Ed McKenzie, 1985. "An Autoregressive Process for Beta Random Variables," Management Science, INFORMS, vol. 31(8), pages 988-997, August.
    • Handle: RePEc:inm:ormnsc:v:31:y:1985:i:8:p:988-997
    DOI: 10.1287/mnsc.31.8.988
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    Citations

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    Cited by:

    1. Abdelhakim Aknouche & Stefanos Dimitrakopoulos, 2023. "Autoregressive conditional proportion: A multiplicative‐error model for (0,1)‐valued time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 393-417, July.
    2. Martinsek, Adam T., 2001. "Sequential estimation of the mean in a random coefficient autoregressive model with beta marginals," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 53-61, January.
    3. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2021. "Autoregressive conditional proportion: A multiplicative-error model for (0,1)-valued time series," MPRA Paper 110954, University Library of Munich, Germany, revised 06 Dec 2021.
    4. Popovic, Bozidar V. & Pogány, Tibor K. & Nadarajah, Saralees, 2010. "On mixed AR(1) time series model with approximated beta marginal," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1551-1558, October.
    5. Melchior, Cristiane & Zanini, Roselaine Ruviaro & Guerra, Renata Rojas & Rockenbach, Dinei A., 2021. "Forecasting Brazilian mortality rates due to occupational accidents using autoregressive moving average approaches," International Journal of Forecasting, Elsevier, vol. 37(2), pages 825-837.
    6. Ronning, Gerd, 1990. "Share equations in econometrics: A story of repression, frustation and dead ends," Discussion Papers, Series II 118, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    7. Wagner Hugo Bonat & Paulo Justiniano Ribeiro & Walmes Marques Zeviani, 2015. "Likelihood analysis for a class of beta mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 252-266, February.
    8. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    9. Martinsek, Adam T., 2002. "Estimation of the maximum and minimum in a model for bounded, dependent data," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 381-393, February.
    10. da-Silva, C.Q. & Migon, H.S. & Correia, L.T., 2011. "Dynamic Bayesian beta models," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2074-2089, June.
    11. Ricardo Rasmussen Petterle & Wagner Hugo Bonat & Cassius Tadeu Scarpin, 2019. "Quasi-beta Longitudinal Regression Model Applied to Water Quality Index Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 346-368, June.
    12. Alice B. V. Mello & Maria C. S. Lima & Abraão D. C. Nascimento, 2022. "A notable Gamma‐Lindley first‐order autoregressive process: An application to hydrological data," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.
    13. Jones, M.C., 2022. "Duals of multiplicative relationships involving beta and gamma random variables," Statistics & Probability Letters, Elsevier, vol. 191(C).
    14. Božidar Popović & Saralees Nadarajah & Miroslav Ristić, 2013. "A new non-linear AR(1) time series model having approximate beta marginals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 71-92, January.
    15. Peluso, Stefano & Mira, Antonietta & Muliere, Pietro, 2015. "Reinforced urn processes for credit risk models," Journal of Econometrics, Elsevier, vol. 184(1), pages 1-12.

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