Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes

We characterize the dynamic properties of Generalized Autoregressive Score (GAS) processes by identifying regions of the parameter space that imply stationarity and ergodicity. We show how these regions are affected by the choice of parameterization and scaling, which are key features of GAS models compared to other observation driven models. The Dudley entropy integral is used to ensure the non-degeneracy of such regions. Furthermore, we show how to obtain bounds for these regions in models for time-varying means, variances, or higher-order moments