IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i1d10.1007_s00362-016-0753-z.html
   My bibliography  Save this article

SYMARMA: a new dynamic model for temporal data on conditional symmetric distribution

Author

Listed:
  • Vinicius Q. S. Maior

    (UFPE)

  • Francisco José A. Cysneiros

    (UFPE)

Abstract

Gaussian models of time series, ARMA, have been widely used in the literature. Benjamin et al. (J Am Stat Assoc 98:214–223, 2003) extended these models to the exponential family distributions. Also in that direction, Rocha and Cribari-Neto (Test 18:529–545, 2009) proposed a time series model for the class of beta distributions. In this paper, we develop an autoregressive and moving average symmetric model, named SYMARMA, which is a dynamic model for random variables belonging to the class of symmetric distributions including also a set of regressors. We discuss methods for parameter estimation, hypothesis testing and forecasting. In particular, we provide closed-form expressions for the score function and Fisher information matrix. Robust study is presented based on influence function. We conduct simulation studies to evaluate the consistency and asymptotic normality of the conditional maximum likelihood estimator for the model parameters. An application with real data is presented and discussed.

Suggested Citation

  • Vinicius Q. S. Maior & Francisco José A. Cysneiros, 2018. "SYMARMA: a new dynamic model for temporal data on conditional symmetric distribution," Statistical Papers, Springer, vol. 59(1), pages 75-97, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0753-z
    DOI: 10.1007/s00362-016-0753-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0753-z
    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/s00362-016-0753-z?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. Manuel Galea & Gilberto Paula & Miguel Uribe-Opazo, 2003. "On influence diagnostic in univariate elliptical linear regression models," Statistical Papers, Springer, vol. 44(1), pages 23-45, January.
    2. Gilberto A. Paula & Víctor Leiva & Michelli Barros & Shuangzhe Liu, 2012. "Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(1), pages 16-34, January.
    3. Gilberto Paula & Francisco Jose Cysneiros, 2009. "Systematic risk estimation in symmetric models," Applied Economics Letters, Taylor & Francis Journals, vol. 16(2), pages 217-221.
    4. Andréa Rocha & Francisco Cribari-Neto, 2009. "Beta autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 529-545, November.
    5. Benjamin M.A. & Rigby R.A. & Stasinopoulos D.M., 2003. "Generalized Autoregressive Moving Average Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 214-223, January.
    6. Pena, Daniel, 1990. "Influential Observations in Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 235-241, April.
    7. Cysneiros, Francisco Jose A. & Paula, Gilberto A., 2005. "Restricted methods in symmetrical linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 689-708, June.
    Full references (including those not matched with items on IDEAS)

    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. Carlos Eduardo M. Relvas & Gilberto A. Paula, 2016. "Partially linear models with first-order autoregressive symmetric errors," Statistical Papers, Springer, vol. 57(3), pages 795-825, September.
    2. Villegas, Cristian & Paula, Gilberto A. & Cysneiros, Francisco José A. & Galea, Manuel, 2013. "Influence diagnostics in generalized symmetric linear models," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 161-170.
    3. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    4. Francisco JA Cysneiros, 2018. "Symmetric Regression Model for Temporal Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 5(2), pages 44-45, February.
    5. Zheng, Tingguo & Chen, Rong, 2017. "Dirichlet ARMA models for compositional time series," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 31-46.
    6. Guilherme Pumi & Taiane Schaedler Prass & Rafael Rigão Souza, 2021. "A dynamic model for double‐bounded time series with chaotic‐driven conditional averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 68-86, March.
    7. Abraão D. C. Nascimento & Maria C. S. Lima & Hassan Bakouch & Najla Qarmalah, 2023. "Scaled Muth–ARMA Process Applied to Finance Market," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    8. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    9. Tingguo Zheng & Han Xiao & Rong Chen, 2022. "Generalized autoregressive moving average models with GARCH errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 125-146, January.
    10. Germán Ibacache-Pulgar & Gilberto Paula & Francisco Cysneiros, 2013. "Semiparametric additive models under symmetric distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 103-121, March.
    11. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
    12. Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.
    13. Palm, Bruna G. & Bayer, Fábio M. & Cintra, Renato J., 2022. "2-D Rayleigh autoregressive moving average model for SAR image modeling," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    14. Alcantara, Izabel Cristina & Cysneiros, Francisco José A., 2013. "Linear regression models with slash-elliptical errors," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 153-164.
    15. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2021. "Autoregressive conditional proportion: A multiplicative-error model for (0,1)-valued time series," MPRA Paper 110954, University Library of Munich, Germany, revised 06 Dec 2021.
    16. Tingguo Zheng & Han Xiao & Rong Chen, 2021. "Generalized Autoregressive Moving Average Models with GARCH Errors," Papers 2105.05532, arXiv.org.
    17. Cribari-Neto, Francisco & Scher, Vinícius T. & Bayer, Fábio M., 2023. "Beta autoregressive moving average model selection with application to modeling and forecasting stored hydroelectric energy," International Journal of Forecasting, Elsevier, vol. 39(1), pages 98-109.
    18. Maia, Gisele de Oliveira & Barreto-Souza, Wagner & Bastos, Fernando de Souza & Ombao, Hernando, 2021. "Semiparametric time series models driven by latent factor," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1463-1479.
    19. Víctor Leiva & Shuangzhe Liu & Lei Shi & Francisco José A. Cysneiros, 2016. "Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 627-642, March.
    20. Abdelhakim Aknouche & Stefanos Dimitrakopoulos, 2023. "Autoregressive conditional proportion: A multiplicative‐error model for (0,1)‐valued time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 393-417, July.

    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:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0753-z. 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.