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