Title: On the first-order integer-valued bilinear model
Authors: Isabel Pereira - University of Aveiro (Portugal) [presenting]
Nelia Silva - University of Aveiro (Portugal)
Abstract: The integer-valued bilinear INBL $(1,0,1,1)$ model is discussed. This class of models is particularly suitable for modeling processes which assume low values with high probability, but exhibiting, at the same time, sudden bursts of large values. However, although the likelihood function is based on convolutions of commonly used distributions, it has a very complex form. In order to overcome this difficulty it is proposed an approach based on saddlepoint techniques to estimate model parameters. It is carried out a simulation study to compare these results with the ones obtained through maximum likelihood method and Bayesian approach. Furthermore, the problem of predicting future observations from the classical and Bayesian approaches is analyzed. Since the evaluation of predictive performance and the suitability of the model are important issues, the probabilistic forecast is compared with the true data-generating distribution. This comparison is made using the Probability Integral Transform (PIT) and applied to real data sets of E.coli infections and meningitis cases.