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Extended dynamic generalized linear models: The two-parameter exponential family

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  • Souza, M.A.O.
  • Migon, H.S.
  • Pereira, J.B.M.

Abstract

A Bayesian framework for estimation and prediction of dynamic models for observations from the two-parameter exponential family is developed. Different link functions are introduced to model both the mean and the precision in the exponential family allowing the introduction of covariates and time series components such as trend and seasonality. Conjugacy and analytical approximations are explored under the class of partially specified models to keep the computation fast. Due to the sequential nature of the proposed algorithm, all the advantages of sequential analysis, such as monitoring and intervention, can be applied to cope with the two-parameter exponential family models. The methodological novelties are illustrated with a simulation study and two applications to real data. The first application considers a well known financial time series regarding IBM stock returns modeled as following a gamma distribution. The second considers macroeconomic variables of the United Kingdom modeled as beta distributed data.

Suggested Citation

  • Souza, M.A.O. & Migon, H.S. & Pereira, J.B.M., 2018. "Extended dynamic generalized linear models: The two-parameter exponential family," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 164-179.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:164-179
    DOI: 10.1016/j.csda.2016.09.008
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    References listed on IDEAS

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    1. Espinheira, Patri­cia L. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2008. "Influence diagnostics in beta regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4417-4431, May.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    3. 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.
    4. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
    5. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    6. Terence Mills, 2010. "Forecasting compositional time series," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(4), pages 673-690, June.
    7. Ospina, Raydonal & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2006. "Improved point and interval estimation for a beta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 960-981, November.
    8. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
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    Cited by:

    1. T. R. Santos, 2018. "A Bayesian GED-Gamma stochastic volatility model for return data: a marginal likelihood approach," Papers 1809.01489, arXiv.org.

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