Open Access
Translator Disclaimer
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

Abstract

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).

Acknowledgments

Part of the work was conducted while Lu was at University of Paris 13. We thank anonymous referees for helpful comments.

Citation

Download Citation

Christian Gouriéroux. Yang Lu. "Noncausal counting processes: A queuing perspective." Electron. J. Statist. 15 (2) 3852 - 3891, 2021. https://doi.org/10.1214/21-EJS1875

Information

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

Digital Object Identifier: 10.1214/21-EJS1875

Subjects:
Primary: 60K25 , 62M10

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

JOURNAL ARTICLE
40 PAGES


SHARE
Vol.15 • No. 2 • 2021
Back to Top