Signed compound poisson integer-valued GARCH processes

Abstract

We propose signed compound Poisson integer-valued GARCH processes for the modeling of the difference of count time series data. We investigate the theoretical properties of these processes and we state their ergodicity and stationarity under mild conditions. We discuss the conditional maximum likelihood estimator when the series appearing in the difference are INGARCH with geometric distribution and explore its finite sample properties in a simulation study. Two real data examples illustrate this methodology.

Keywords:

• Integer-valued time series
• GARCH model
• compound Poisson distributions

Acknowledgments

The authors are grateful to the referees and the Editor in Chief for insightful comments and suggestions.

Additional information

Funding

This work was supported by the Center for Mathematics of the University of Coimbra - UID/MAT/00324/2019 funded by the Portuguese Government trough FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.