17 research outputs found
Inference for bivariate integer-valued moving average models based on binomial thinning operation
Time series of (small) counts are common in practice and appear in a wide variety of fields. In the last three decades, several models that explicitly account for the discreteness of the data have been proposed in the literature. However, for multivariate time series of counts several difficulties arise and the literature is not so detailed. This work considers Bivariate INteger-valued Moving Average, BINMA, models based on the binomial thinning operation. The main probabilistic and statistical properties of BINMA models are studied. Two parametric cases are analysed, one with the cross-correlation generated through a Bivariate Poisson innovation process and another with a Bivariate Negative Binomial innovation process. Moreover, parameter estimation is carried out by the Generalized Method of Moments. The performance of the model is illustrated with synthetic data as well as with real datasets.publishe
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