Modelling overdispersion with integer-valued moving average processes

A new first-order integer-valued moving average, INMA(1), model based on the negative binomial thinning operation defined by Risti´c et al. [21] is proposed and characterized. It is shown that this model has negative binomial (NB) marginal distribution when the innovations follow a NB distribution and therefore it can be used in situations where the data present overdispersion. Additionally, this model is extended to the bivariate context. The Generalized Method of Moments (GMM) is used to estimate the unknown parameters of the proposed models and the results of a simulation study that intends to investigate the performance of the method show that, in general, the estimates are consistent and symmetric. Finally, the proposed model is fitted to a real dataset and the quality of the adjustment is evaluated.publishe

On the theory of periodic multivariate INAR processes

In this paper a multivariate integer-valued autoregressive model of order one with periodic time-varying parameters, and driven by a periodic innovations sequence of independent random vectors is introduced and studied in detail. Emphasis is placed on models with periodic multivariate negative binomial innovations. Basic probabilistic and statistical properties of the novel model are discussed. Aiming to reduce computational burden arising from the use of the conditional maximum likelihood method, a composite likelihood-based approach is adopted. The performance of such method is compared with that of some traditional competitors, namely moment estimators and conditional maximum likelihood estimators. Forecasting is also addressed. Furthermore, an application to a real data set concerning the monthly number of fires in three counties in Portugal is presented.publishe