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A skew-normal dynamic linear model and Bayesian forecasting

Author

Listed:
  • Reinaldo B. Arellano-Valle

    (Pontificia Universidad Católica de Chile)

  • Javier E. Contreras-Reyes

    (Universidad de Valparaíso)

  • Freddy O. López Quintero

    (Compañía de Telecomunicaciones de Chile S.A.)

  • Abel Valdebenito

    (Pontificia Universidad Católica de Chile)

Abstract

Dynamic linear models are typically developed assuming that both the observational and system distributions are normal. In this work, we relax this assumption by considering a skew-normal distribution for the observational random errors, providing thus an extension of the standard normal dynamic linear model. Full Bayesian inference is carried out using the hierarchical representation of the model. The inference scheme is led by means of the adaptation of the Forward Filtering Backward sampling and the usual MCMC algorithms to perform the inference. The proposed methodology is illustrated by a simulation study and applied to the condition factor index of male and female anchovies off northern Chile. These indexes have not been studied in a dynamic linear model framework.

Suggested Citation

  • Reinaldo B. Arellano-Valle & Javier E. Contreras-Reyes & Freddy O. López Quintero & Abel Valdebenito, 2019. "A skew-normal dynamic linear model and Bayesian forecasting," Computational Statistics, Springer, vol. 34(3), pages 1055-1085, September.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-0848-1
    DOI: 10.1007/s00180-018-0848-1
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    References listed on IDEAS

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    1. Cabral, Celso Rômulo Barbosa & da-Silva, Cibele Queiroz & Migon, Helio S., 2014. "A dynamic linear model with extended skew-normal for the initial distribution of the state parameter," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 64-80.
    2. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
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    6. Kim, Hyoung-Moon & Ryu, Duchwan & Mallick, Bani K. & Genton, Marc G., 2014. "Mixtures of skewed Kalman filters," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 228-251.
    7. Naveau, Philippe & Genton, Marc G. & Shen, Xilin, 2005. "A skewed Kalman filter," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 382-400, June.
    8. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
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