Processo Skellam INAR(1) assimétrico

Abstract

Time series of counts have been a very explored theme in the past decades due to the importance of the application in several practical situations. In this work an asymmetric version of Freeland (2010) model is proposed. In order to model these time series, an autoregressive stationary process of first order (INAR(1)) will be constructed for integer values with the asymmetric Skellam as marginal distribution. Properties of this model will be studied and demonstrated, such as the conditional distribution, the two variable joint distribution Zt and Ztk, covariance, conditional moment generating function and also conditional mean and variance. The parameters of the model will be estimated based on conditional least squares estimator. It will also be verified the consistencyand the asymptotic normality of the estimators. The behavior of the estimators will be evaluated via Monte Carlo simulation. The master thesis will be completed by applying the proposed INAR(1) model to a real time series.