Generalized Autoregressive Score Models with Applications

University of Chicago Booth School of Business, Chicago, IL, USA; Department of Econometrics, VU University Amsterdam, Netherlands; Department of Finance, VU University Amsterdam, and Duisenberg School of Finance, Amsterdam, Netherlands; Tinbergen Institute, Amsterdam, Netherlands
Journal of Applied Econometrics (Impact Factor: 1.76). 01/2012; DOI: 10.1002/jae.1279

ABSTRACT We propose a class of observation-driven time series models referred to as generalized autoregressive score (GAS) models. The mechanism to update the parameters over time is the scaled score of the likelihood function. This new approach provides a unified and consistent framework for introducing time-varying parameters in a wide class of nonlinear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, autoregressive conditional duration, autoregressive conditional intensity, and Poisson count models with time-varying mean. In addition, our approach can lead to new formulations of observation-driven models. We illustrate our framework by introducing new model specifications for time-varying copula functions and for multivariate point processes with time-varying parameters. We study the models in detail and provide simulation and empirical evidence. Copyright © 2012 John Wiley & Sons, Ltd.

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    ABSTRACT: We characterize the dynamic properties of generalized autore-gressive 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 param-eterization 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. MSC 2010 subject classifications: Primary 60G10, 62M10; secondary 91B84.
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