Highly Flexible Poisson–Tweedie Integer‐Valued GARCH Models With Automatic Adaptation to Dispersion

ABSTRACT This paper presents a more flexible and generic integer‐valued GARCH model, designed to automatically adapt to dispersion for modelling count time series. Strict stationarity and ergodicity are established using weak dependence theory. Estimators are obtained via quasi‐maximum likelihood and Pearson estimating functions. Under mild regularity conditions, strong consistency and asymptotic normality are formally derived. Monte Carlo simulations confirm our theorems and assess the performance of unknown parameters in finite samples. Two empirical examples are analysed to demonstrate the model's superiority. Methods for model extension and improvement in cases of negative correlation and outliers are explored. Copyright © 2025 John Wiley & Sons, Ltd.