Generalized autoregressive score models based on sinh-arcsinh distributions for time series analysis

Models with time-varying parameters have become more popular for time series analysis. Among these models, Generalized Autoregressive Score (GAS) models are based on the specification of the mechanism through which past observations of the variable of interest affect the current value of the time-varying parameters. GAS models allow capturing the dynamic behavior of time series processes, which is an advantage over models such as ARMA and GARCH with fixed parameters. In this paper, we extend the distribution setting of GAS models from classical densities to sinh-arcsinh (SAS) ones, with emphasis on SAS-Gaussian and SAS-t distribution. The SAS family provides flexible distributions that allow modeling the asymmetry as light or heavy tailed. The parameters of the family enable clear interpretations, and limiting distributions are especially appealing as shape parameters tend to their extreme values. The proposed method's performance is illustrated in simulations and a real-world application to a fish condition dataset. In conclusion, the SAS-Gaussian distribution fits the dataset best by far.