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The aim this study is discussed on the detection and correction of data containing the additive outlier (AO) on the model ARIMA (p, d, q). The process of detection and correction of data using an iterative procedure popularized by Box, Jenkins, and Reinsel (1994). By using this method we obtained an ARIMA models were fit to the data containing AO, this model is added to the original model of ARIMA coefficients obtained from the iteration process using regression methods. In the simulation data is obtained that the data contained AO initial models are ARIMA (2,0,0) with MSE = 36,780, after the detection and correction of data obtained by the iteration of the model ARIMA (2,0,0) with the coefficients obtained from the regression       1 2 1 2 3 0,106 0, 204 0, 401 329 115 35,9 t t t Z Z Z X t X t X t         and MSE = 19,365. This shows that there is an improvement of forecasting error rate data.

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Model selection in neural networks can be guided by statistical procedures, such as hypothesis tests, information criteria and cross validation. Taking a statistical perspective is especially important for nonparametric models like neural networks, because the reason for applying them is the lack of knowledge about an adequate functional form. Many researchers have developed model selection strategies for neural networks which are based on statistical concepts. In this paper, we focused on the model evaluation by implementing statistical significance test. We used Wald-test to evaluate the relevance of parameters in the networks for classification problem. Parameters with no significance influence on any of the network outputs have to be removed. In general, the results show that Wald-test work properly to determine significance of each weight from the selected model. An empirical study by using Iris data yields all parameters in the network are significance, except bias at the first output neuron.

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In this paper we investigated the asymptotic distribution of the bootstrap parameter estimator of a first order autoregressive AR(1) model. We described the asymptotic distribution of such estimator by applying the delta method and employing two different approaches, and concluded that the two approaches lead to the same conclusion, viz. both results converge in distribution to a normal distribution. We also presented the Monte Carlo simulation of the residuals bootstrap and application with real data was carried out in order to yield apparent conclusions.