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A flexible two-piece normal dynamic linear model

Author

Listed:
  • Emanuele Aliverti

    (Università di Padova)

  • Reinaldo B. Arellano-Valle

    (Pontificia Universidad Católica de Chile)

  • Fereshteh Kahrari

    (Università di Padova)

  • Bruno Scarpa

    (Università di Padova
    Università di Padova)

Abstract

We construct a flexible dynamic linear model for the analysis and prediction of multivariate time series, assuming a two-piece normal initial distribution for the state vector. We derive a novel Kalman filter for this model, obtaining a two components mixture as predictive and filtering distributions. In order to estimate the covariance of the error sequences, we develop a Gibbs-sampling algorithm to perform Bayesian inference. The proposed approach is validated and compared with a Gaussian dynamic linear model in simulations and on a real data set.

Suggested Citation

  • Emanuele Aliverti & Reinaldo B. Arellano-Valle & Fereshteh Kahrari & Bruno Scarpa, 2023. "A flexible two-piece normal dynamic linear model," Computational Statistics, Springer, vol. 38(4), pages 2075-2096, December.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:4:d:10.1007_s00180-023-01355-3
    DOI: 10.1007/s00180-023-01355-3
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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. T. R. A. Corns & S. E. Satchell, 2007. "Skew Brownian Motion and Pricing European Options," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 523-544.
    3. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi & Ferreira, Clécio S. & Santoro, Karol, 2020. "A two-piece normal measurement error model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    4. Fasano, Augusto & Rebaudo, Giovanni & Durante, Daniele & Petrone, Sonia, 2021. "A closed-form filter for binary time series," MPRA Paper 122349, University Library of Munich, Germany.
    5. 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.
    6. Naveau, Philippe & Genton, Marc G. & Shen, Xilin, 2005. "A skewed Kalman filter," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 382-400, June.
    7. 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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