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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
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    References listed on IDEAS

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    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)

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