Noncausal counting processes: A queuing perspective

We introduce noncausal counting processes, defined by time-reversing an INAR(1) process, a non-INAR(1) Markov affine or random coefficient [RCINAR(1)] process. The processes are shown to be generically time irreversible and their calendar dynamic properties unreplicable existing causal models. In particular, they allow for locally bubble-like explosion, while at the same preserving stationarity. Many of these have also closed form conditional predictive distribution, simple queuing interpretation, similar as counterparts.