A Positive and Negative Integer-valued Bilinear Type Process
Résumé
With the aim of generalizing a bilinear type counting model, we redefine a more elaborated model than the one proposed by Doukhan et al. (2006). This new model, which can be useful in a context of inventory management or epidemiology, is based on a thinning operator allowing for negative values. In a simple way, we demonstrate the existence of such a process. The estimation of the parameters is tackled with the help of a quasi-maximum likelihood approach (referred to as QMLE). Under certain hypotheses, we prove that these QMLE estimators are strongly convergent. With some additionnal assumptions, we obtain asymptotically normal estimators