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The purpose of this paper is to develop a Bayesian analysis for the zeroinflated hyper-Poisson model. Markov chain Monte Carlo methods are used to develop a Bayesian procedure for the model and the Bayes estimators are compared by simulation with the maximum-likelihood estimators. Regression modeling and model selection are also discussed and case deletion influence diagnostics are developed for the joint posterior distribution based on the functional Bregman divergence, which includes ψ-divergence and several others, divergence measures, such as the Itakura-Saito, Kullback-Leibler, and χ 2 divergence measures. Performance of our approach is illustrated in artificial, real apple cultivation experiment data, related to apple cultivation.

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A growing field is related to automatized Time Series analysis, through complicated due to the dependence of observed and hidden dimensions often presented in these data types. In this report the problem is motivated by a Brazilian financial company interested in unraveling relation structure explanation of the Japanese' CPI ex-fresh Food \& Energy across 157 economical exogenous variables, with very limiting data. The problem becomes more complex when considering that each variable can enter the model with lags of 0 to 8 periods, as well as an additional restriction of admitting only a positive relationship. This report discusses three possible treatments involving models for structured time series, the most relevant approach found in this study is a Dynamic Regression Model combined with a Stepwise algorithm, which allows the most relevant variables, as well as their respective lags, to be found and inserted in the model with low computational cost.

Parametric autoregressive moving average models with exogenous terms (ARMAX) have been widely used in the literature. Usually, these models consider a conditional mean or median dynamics, which limits the analysis. In this paper, we introduce a class of quantile ARMAX models based on log-symmetric distributions. This class is indexed by quantile and dispersion parameters. It not only accommodates the possibility to model bimodal and/or light/heavy-tailed distributed data but also accommodates heteroscedasticity. We estimate the model parameters by using the conditional maximum likelihood method. Furthermore, we carry out an extensive Monte Carlo simulation study to evaluate the performance of the proposed models and the estimation method in retrieving the true parameter values. Finally, the proposed class of models and the estimation method are applied to a dataset on the competition "M5 Forecasting -Accuracy" that corresponds to the daily sales history of several Walmart products. The results indicate that the proposed log-symmetric quantile ARMAX models have good performance in terms of model fitting and forecasting.