A geometric time series model with inflated-parameter Bernoulli counting series

In this paper, we propose a new stationary first-order non-negative integer valued autoregressive [INAR(1)] process with geometric marginals based on a modified version of the binomial thinning operator. This new process will enable one to tackle the problem of overdispersion inherent in the analysis of integer-valued time series data that may arise due to the presence of some correlation between underlying events, heterogeneity of the population, excess to zeros, among others. In addition, it includes as special cases the geometric INAR(1) [GINAR(1)] (Alzaid and Al-Osh, 1988) and new geometric [NGINAR(1)] (Ristić et al., 2009) processes, making it be very useful in discriminating between nested models. The innovation structure of the new process is very simple. The main properties of the process are derived, such as conditional distribution, autocorrelation structure, innovation structure and jumps. The method of conditional maximum likelihood is used for estimating the process parameters. Some numerical results of the estimators are presented with a brief discussion. In order to illustrate the potential for practice of our process we apply it to a real data set.