Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes
Tinbergen Institute Discussion Paper No. 12-059/2
31 Pages Posted: 22 Jun 2012 Last revised: 20 Mar 2014
Date Written: June 21, 2012
Abstract
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.
Keywords: Dudley integral, Durations, Higher-order models, Nonlinear dynamics, Time-varying parameters, Volatility
JEL Classification: C13, C22, C58
Suggested Citation: Suggested Citation
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