Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes

Francisco Blasques (), Siem Jan Koopman and Andre Lucas

No 12-059/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This discussion paper led to a publication in the Electronic Journal of Statistics , 2014, 8, 1088-1112.

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 (search for similar items in EconPapers)
JEL-codes: C13 C22 C58 (search for similar items in EconPapers)
Date: 2012-06-22
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20120059

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