Electronic Journal of Statistics

Stationarity and ergodicity of univariate generalized autoregressive score processes

Francisco Blasques, Siem Jan Koopman, and André Lucas

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We characterize the dynamic properties of generalized autoregressive score models by identifying the regions of the parameter space that imply stationarity and ergodicity of the corresponding nonlinear time series process. We show how these regions are affected by the choice of parameterization and scaling, which are key features for the class of generalized autoregressive score models compared to other observation driven models. All results are illustrated for the case of time-varying means, variances, or higher-order moments.

Article information

Electron. J. Statist., Volume 8, Number 1 (2014), 1088-1112.

First available in Project Euclid: 5 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G10: Stationary processes 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 91B84: Economic time series analysis [See also 62M10]

Nonlinear dynamics observation driven time-varying parameter models stochastic recurrence equations contracting properties


Blasques, Francisco; Koopman, Siem Jan; Lucas, André. Stationarity and ergodicity of univariate generalized autoregressive score processes. Electron. J. Statist. 8 (2014), no. 1, 1088--1112. doi:10.1214/14-EJS924. https://projecteuclid.org/euclid.ejs/1407243244

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