We introduce noncausal counting processes, defined by time-reversing an INAR(1) process, a non-INAR(1) Markov affine counting process, or a random coefficient INAR(1) [RCINAR(1)] process. The noncausal processes are shown to be generically time irreversible and their calendar time dynamic properties are unreplicable by existing causal models. In particular, they allow for locally bubble-like explosion, while at the same time preserving stationarity. Many of these processes have also closed form calendar time conditional predictive distribution, and allow for a simple queuing interpretation, similar as their causal counterparts.
Gouriéroux gratefully acknowledges the financial support of the ACPR/Risk Foundation Chair: Regulation and Systemic Risk, and the ERC DYSMOIA. Lu thanks support from CNRS, the Labex MME-DII and Concordia University (Start-up grant).
Part of the work was conducted while Lu was at University of Paris 13. We thank anonymous referees for helpful comments.
"Noncausal counting processes: A queuing perspective." Electron. J. Statist. 15 (2) 3852 - 3891, 2021. https://doi.org/10.1214/21-EJS1875