Novos modelos para séries temporais de valores binários e inteiros não negativos baseados em operadores thinning

Abstract

Models for time series of integer values have stood out because of the vast possibility of application. Models for statistical process control, for economic data and currently for the structural sequence of deoxyribonucleic acids (DNA) are examples of important applications. This work is divided into two independent parts. The first part of the work concerns the modeling of autocorrelated binary data. In this context, a new class of models has been proposed, based on thinning operators called Bernoulli autoregressive process of order p [BeAr(p)] similar to the classical model AR(p). In particular, BeAr(1) model was studied, various properties of three estimation methods have been proposed for the model, including the asymptotic distribution of the estimators by the conditional least squares method, and the elements of the Fisher information matrix. In addition to the simulations, applications were made on real data of precipitation, at which models BeAr(1) and BeAr(2) were given to modeling. In the second part of the work, new models were studied to propose the family of inflated-parameter generalized power series distributions (IGPSD) to the innovation process INAR(1) model. The main properties of the process have been established, such as the mean, variance, autocorrelation and transition probability. The estimation methods for Yule-Walker and conditional maximum likelihood were used to estimate the parameters of the models. Two particular cases of model INAR(1) with IGPSD innovation process were studied, called IPoINAR(1) and IGeoINAR(1). Applications to real data showed a good performance of the new model proposed.