Open Access
2021 Noncausal counting processes: A queuing perspective
Christian Gouriéroux, Yang Lu
Author Affiliations +
Electron. J. Statist. 15(2): 3852-3891 (2021). DOI: 10.1214/21-EJS1875


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.

Funding Statement

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.


Download Citation

Christian Gouriéroux. Yang Lu. "Noncausal counting processes: A queuing perspective." Electron. J. Statist. 15 (2) 3852 - 3891, 2021.


Received: 1 May 2020; Published: 2021
First available in Project Euclid: 29 July 2021

Digital Object Identifier: 10.1214/21-EJS1875

Primary: 60K25 , 62M10

Keywords: Discrete stable distribution , infinite server queue , Noncausal process , Time reversibility bubble

Vol.15 • No. 2 • 2021
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