Hyper-parametric Generalized Autoregressive Scores (GASs): an application to the price of United States cooking gas

This paper presents the framework of the Generalized Autoregressive Score (GAS) model with a variety of symmetric conditional densities of different time-varying hyperparameters. The distinctive trait and goal of the observation-driven GAS model is to use its score and information functions as the compeller of time-variation via hyper-parameters of conditional densities. 10 robust hyper-parametric conditional densities were used as random error drivers for the GAS model with an application to the price of the United States cooking gas in the period between 2005 and 2020. Out of the 10 robust hyper-parametric conditional noises for the GAS model, the Asymmetric Student–t with one tail decay parameter (AST1) outperformed other categories of its variants and other conditional densities subjected to the GAS model, achieving a minimum reduced-error performance of AIC=11943.277 and BIC=12014.525. The hyper-parametric model obtained a location score and scale score of - 1.2634 and 0.6636, respectively, while its location information and scale information was 0.2691 and 0.0362, respectively. Furthermore, the GAS model via AST1 proved more efficient than the core volatile conditional heteroscedasticity model of the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) at GARCH (1,1) via a Gaussian distributed noise.