Modelos para séries temporais utilizando as distribuições normal generalizada e log-normal generalizada
Milani, Eder Angelo
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From the generalized normal distribution and concepts of the generalized autoregressive moving averages models we introduce the generalized normal-ARMA model as an alternative way to model time series exhibiting symmetry and tails that may be lighter or heavier when compared the normal distribution. We present application for proposed model using three time series in the hydrology, economy and publics policy areas. The proposed model is presented as good alternative when compared to ARMA model with normal distribution. We extended this model the case of the asymmetric time series. In this case we used the Box-Cox transformation, denoted by Box-Cox generalized normal ARMA. The particular case, when we use the logarithmic transformation is called generalized log-normal ARMA. We adjusted the models with transformation to the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants. We obtain the prediction values for the model with transformation, that are better when compared with the model without transformation. To treat time series that exhibit periodic in the correlation function we defined three extensions for periodic autoregressive model, called generalized normal periodic autoregressive model, generalized log-normal periodic autoregressive model and Box-Cox generalized normal periodic autoregressive model. We can observed that the series on monthly average affluent streamflow of the Furnas and Sobradinho hydroelectric plants have periodic correlation. We present two applications of periodic models from these series. In the models, we note that is not necessary the use of generalized normal distribution in every months, just in some the generalized normal distribution presented better results than the normal distribution. Finally, we define the generalized normal zero inflated distribution and the generalized normal zero inflated ARMA model for time series. Adopting the model for series that have zero inflation and the maximum likelihood method for estimation of parameters, we analyze the serie of the amount of rainfall in the city of São Carlos.
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Jesus, Sandra Rêgo de; http://lattes.cnpq.br/0092258556747592 (Universidade Federal de São Carlos, UFSCar, Programa de Pós-Graduação em Estatística - PPGEs, , 21/11/2014)The Generalized Normal (GN) and Generalized lognormal (logGN) distributions are flexible for accommodating features present in the data that are not captured by traditional distribution, such as the normal and the lognormal ...
Mamani Bustamante, Juan Pablo; http://lattes.cnpq.br/9245409946336145 (Universidade Federal de São Carlos, UFSCar, Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs, , 25/02/2015)The identification of influential and/or atypical observations in a data set is known as a part of the diagnostic analysis. One of the purposes of the diagnostic analysis is to verify the robustness of a statistical model, ...
Fernandes, Victor Vinicius; http://lattes.cnpq.br/1671975353265972 (Universidade Federal de São Carlos, UFSCar, Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs, Câmpus São Carlos, 30/04/2019)The simulated envelope is a diagnostic analysis method used to evaluate the hypothesis about the probability distribution assumed for the response variable in a regression model. In this work, we describe some procedures ...