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

See all articles by Francisco Blasques

Francisco Blasques

VU University Amsterdam; Tinbergen Institute

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Andre Lucas

Vrije Universiteit Amsterdam; Tinbergen Institute

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

Blasques, Francisco and Blasques, Francisco and Koopman, Siem Jan and Lucas, Andre, Stationarity and Ergodicity of Univariate Generalized Autoregressive Score Processes (June 21, 2012). Tinbergen Institute Discussion Paper No. 12-059/2, Available at SSRN: https://ssrn.com/abstract=2089452 or http://dx.doi.org/10.2139/ssrn.2089452

Francisco Blasques (Contact Author)

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Andre Lucas

Vrije Universiteit Amsterdam ( email )

SBE/EDS, De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31 20 598 6039 (Phone)
+31 20 598 6020 (Fax)

HOME PAGE: http://personal.vu.nl/a.lucas

Tinbergen Institute

Roetersstraat 31
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.tinbergen.nl

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