Generalized Poisson difference autoregressive processes

Giulia Carallo, Roberto Casarin and Christian P. Robert

International Journal of Forecasting, 2024, vol. 40, issue 4, 1359-1390

Abstract: This paper introduces a novel stochastic process with signed integer values. Its autoregressive dynamics effectively captures persistence in conditional moments, rendering it a valuable feature for forecasting applications. The increments follow a Generalized Poisson distribution, capable of accommodating over- and under-dispersion in the conditional distribution, thereby extending standard Poisson difference models. We derive key properties of the process, including stationarity conditions, the stationary distribution, and conditional and unconditional moments, which prove essential for accurate forecasting. We provide a Bayesian inference framework with an efficient posterior approximation based on Markov Chain Monte Carlo. This approach seamlessly incorporates inherent parameter uncertainty into predictive distributions. The effectiveness of the proposed model is demonstrated through applications to benchmark datasets on car accidents and an original dataset on cyber threats, highlighting its superior fitting and forecasting capabilities compared to standard Poisson models.

Keywords: Bayesian inference; Counts time series; Cyber risk; GARCH models; Poisson processes (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0169207023001310
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Generalized Poisson Difference Autoregressive Processes (2020)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:intfor:v:40:y:2024:i:4:p:1359-1390

DOI: 10.1016/j.ijforecast.2023.11.009

Access Statistics for this article

International Journal of Forecasting is currently edited by R. J. Hyndman

More articles in International Journal of Forecasting from Elsevier
Bibliographic data for series maintained by Catherine Liu ().