A note about the delta-moment in ARMA-APARCH models with stable conditional distributions and GEV


  • Thiago R. Sousa Departamento de Estatística, UnB, 70910-900 Brasília, DF, Brazil
  • Cira E. G. Otiniano Departamento de Estatística, UnB, 70910-900 Brasília, DF, Brazil
  • Silvia R. C. Lopes Departmento de Matemática,Universidade Federal de Rio Grande do Sul, Brazil




ARMA, GARCH, APARCH, Stationarity, Stable distribution, GEV distribution


In a ARMA-APARCH time series model with innovations Z, the delta-stationarity condition of the APARCH process involves the delta-th moment of the difference between the absolute value of the innovations with the product of the asymmetry parameter and the innovations. This moment allows calculating more efficiently the estimates of the parameters of the model by maximum likelihood. In this article, we obtain explicit expressions of this delta - th moment where Z has stable and GEV distribution. These moments have been implemented in our GEVStableGarch package available in CRAN R-PROJECT developed to estimate the parameters of ARMA-GARCH / APARCH models with stable innovations and GEV.


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How to Cite

Sousa, T. R., G. Otiniano, C. E., & C. Lopes, S. R. (2018). A note about the delta-moment in ARMA-APARCH models with stable conditional distributions and GEV. Selecciones Matemáticas, 5(01), 7 - 16. https://doi.org/10.17268/sel.mat.2018.01.02