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This paper studies monthly precipitation time series in Viçosa MG, Brazil. We aimed to detect serial patterns in precipitation like trend and seasonality and make predictions for the 2019 year. The idea was to understand water shortage events that occur in Viçosa as well as the challenges regarding water supply for human consumption and agricultural production faced by urban and rural citizens. We used time series and SARIMA (1,0,0) x (0,1,1) model approaches selected based on Bayesian and Akaike Information criteria values (BIC and AIC, respectively). In addition, the ARCH (2) model, selected through AIC, was used to fit SARIMA (1,0,0) x (0,1,1) residues with heteroscedasticity. Our results reveal no changes in precipitation for Viçosa, MG, Brazil, with large variations observed only for specific periods.

The simulation of random correlation matrices is an important procedure in different research areas. This study presents a method called Custom Matrix generator, which generates correlation matrices that always fulfill the appropriate mathematical conditions. In addition, we present an algorithm based on this method which can generate customized correlation matrices for different applications used in several studies. The method is efficient in terms of computational time and it minimizes errors in the process of generating customized correlation matrices.

Methodologies for identifying multivariate outliers are extremely important in statistical analysis. Outliers may reveal relevant information to variables under investigation. Statistical applications without prior identification of possible extreme values may yield controversial results and induce mistaken decision making. In many contexts, outliers are points of great practical interest. Given this, this paper seeks to discuss methodologies for the detection of multivariate outliers through a fair and adequate comparative technique in their simulation procedure. The comparison considers detection techniques based on Mahalanobis distance, besides a methodology based on cluster analysis technique. Sensitivity, specificity, and accuracy metrics are used to measure the method quality. An analysis of the computational time required to perform the procedures is evaluated. The technique based on cluster analysis revealed a noticeable superiority over the others in detection quality and also in execution time.