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A dynamic linear model with extended skew-normal for the initial distribution of the state parameter

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  • Cabral, Celso Rômulo Barbosa
  • da-Silva, Cibele Queiroz
  • Migon, Helio S.

Abstract

We develop a Bayesian dynamic model for modeling and forecasting multivariate time series relaxing the assumption of normality for the initial distribution of the state space parameter, and replacing it by a more flexible class of distributions, which we call Generalized Skew-Normal (GSN) Distributions. We develop a version of the classic Kalman filter, again obtaining GSN predictive and filtering distributions. As we are supposing the random fluctuations covariances to be unknown, a Gibbs-type sampler algorithm is developed in order to perform Bayesian inference. We work with two simulation experiments with scenarios close to real problems in order to show the efficacy of our proposed model. Finally, we apply our technique to a real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:74:y:2014:i:c:p:64-80
    DOI: 10.1016/j.csda.2013.12.008
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    References listed on IDEAS

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    1. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
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    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
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    6. Petris, Giovanni, 2010. "An R Package for Dynamic Linear Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i12).
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    11. 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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    Cited by:

    1. Guljanov, Gaygysyz & Mutschler, Willi & Trede, Mark, 2022. "Pruned Skewed Kalman Filter and Smoother: With Application to the Yield Curve," Dynare Working Papers 78, CEPREMAP.
    2. 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.

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