Fitting poisson time-series models using bivariate mixture transition distributions

Using bivariate mixture transition models (BMTD) in modeling marked points processes (MMP) needs clever reparameterization in an effort to incorporate lag information for capturing the structure of the process being modeled. Such reparameterizations may depend on domain knowledge as well as on considerations of computational stability and prediction capability, among others. A choice of a reasonable reparameterization is needed to build in the lag information, whether linear or nonlinear, and to obtain better results in terms of model stability and prediction capability. This article tackles this issue. Several stable choices of these reparameterizations for the bivariate continuous-discrete BMTD model proposed by Hassan and El-Bassiouni (2012) are considered and compared using a real data set on Internet network traffic. Results show that the inference based on BMTD models is not sensitive to the choice of the functional form as long as such functions involve some carefully chosen exponential forms of the lagged data.