Generalized autoregressive score models with applications

TLDR: A unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models, referred to as Generalized Autoregressive Score (GAS) models, which encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity.

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 non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, the autoregressive conditional duration, the 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.