Generalized Autoregressive Score Models with Applications

Department of Finance, VU University Amsterdam, and Duisenberg School of Finance, Amsterdam, Netherlands
Journal of Applied Econometrics (Impact Factor: 1.76). 08/2013; 28(5). DOI: 10.1002/jae.1279


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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    • "The alternative class of observation-driven models, by contrast, allows parameters to vary over time as functions of lagged dependent variable values and exogenous variables. By way of an example, the recently introduced Generalized Autoregressive Score (GAS) models (Creal et al., 2013), also known as Dynamic Conditional Score (DCS) models, also provide a general framework for modelling time variation in parametric models as functions of lagged dependent variables and exogenous variables (see also Creal et al., 2011). Thus, the GAS model is an observation-driven time series model assuming that we can compute the score of the parametric conditional observation density with respect to the time varying parameter. "
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    • "For other possible choices of a we refer to Creal et al. (2013). "
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