IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v34y2019i3d10.1007_s00180-018-0848-1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-018-0848-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00180-018-0848-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Naveau, Philippe & Genton, Marc G. & Shen, Xilin, 2005. "A skewed Kalman filter," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 382-400, June.
    2. 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.
    3. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    4. Gamerman, Dani & Moreira, Ajax R. B., 2004. "Multivariate spatial regression models," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 262-281, November.
    5. 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.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. Rezaie, Javad & Eidsvik, Jo, 2014. "Kalman filter variants in the closed skew normal setting," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 1-14.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gaygysyz Guljanov & Willi Mutschler & Mark Trede, 2022. "Pruned Skewed Kalman Filter and Smoother: With Application to the Yield Curve," CQE Working Papers 10122, Center for Quantitative Economics (CQE), University of Muenster.
    2. Haiyang Zhang & Chenglin Wen, 2024. "A Higher-Order Extended Cubature Kalman Filter Method Using the Statistical Characteristics of the Rounding Error of the System Model," Mathematics, MDPI, vol. 12(8), pages 1-16, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gaygysyz Guljanov & Willi Mutschler & Mark Trede, 2022. "Pruned Skewed Kalman Filter and Smoother: With Application to the Yield Curve," CQE Working Papers 10122, Center for Quantitative Economics (CQE), University of Muenster.
    2. 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.
    3. Hanze Zhang & Yangxin Huang, 2020. "Quantile regression-based Bayesian joint modeling analysis of longitudinal–survival data, with application to an AIDS cohort study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 339-368, April.
    4. Zhongwei Zhang & Reinaldo B. Arellano‐Valle & Marc G. Genton & Raphaël Huser, 2023. "Tractable Bayes of skew‐elliptical link models for correlated binary data," Biometrics, The International Biometric Society, vol. 79(3), pages 1788-1800, September.
    5. Marjan Mansourian & Anoshirvan Kazemnejad & Iraj Kazemi & Farid Zayeri & Masoud Soheilian, 2012. "Bayesian analysis of longitudinal ordered data with flexible random effects using McMC: application to diabetic macular Edema data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1087-1100, November.
    6. Lin, Tsung I. & Ho, Hsiu J. & Chen, Chiang L., 2009. "Analysis of multivariate skew normal models with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2337-2351, November.
    7. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    8. 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.
    9. M. Teimourian & T. Baghfalaki & M. Ganjali & D. Berridge, 2015. "Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2233-2256, October.
    10. Massimo Bilancia & Giacomo Demarinis, 2014. "Bayesian scanning of spatial disease rates with integrated nested Laplace approximation (INLA)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 71-94, March.
    11. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    12. Lourdes Montenegro & Víctor Lachos & Heleno Bolfarine, 2010. "Inference for a skew extension of the Grubbs model," Statistical Papers, Springer, vol. 51(3), pages 701-715, September.
    13. Alexandra Schmidt & Ajax Moreira & Steven Helfand & Thais Fonseca, 2009. "Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 31(2), pages 101-112, April.
    14. Reinaldo B. Arellano-Valle & Adelchi Azzalini, 2022. "Some properties of the unified skew-normal distribution," Statistical Papers, Springer, vol. 63(2), pages 461-487, April.
    15. Reinaldo B. Arellano-Valle, 2010. "On the information matrix of the multivariate skew-t model," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 371-386.
    16. Arellano-Valle, Reinaldo B. & Genton, Marc G. & Loschi, Rosangela H., 2009. "Shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 91-101, January.
    17. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.
    18. F. Kahrari & C. S. Ferreira & R. B. Arellano-Valle, 2019. "Skew-Normal-Cauchy Linear Mixed Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 185-202, December.
    19. Kheradmandi, Ameneh & Rasekh, Abdolrahman, 2015. "Estimation in skew-normal linear mixed measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 1-11.
    20. Yin, Chuancun & Balakrishnan, Narayanaswamy, 2024. "Stochastic representations and probabilistic characteristics of multivariate skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 199(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-0848-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.