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

Vinicius Q. S. Maior () and Francisco José A. Cysneiros ()
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Vinicius Q. S. Maior: UFPE
Francisco José A. Cysneiros: UFPE

Statistical Papers, 2018, vol. 59, issue 1, No 4, 75-97

Abstract: 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.

Keywords: Conditional maximum likelihood; Outlier; Symmetric distributions; Time series (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00362-016-0753-z

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