Evaluating the performance of degrees of freedom estimation in asymmetric GARCH models with t-student innovations

Abstract

This work investigates the effects of using the independent Jeffreys prior for the degrees of freedom parameter of a t-student model in the asymmetric generalised autoregressive conditional heteroskedasticity (GARCH) model. To capture asymmetry in the reaction to past shocks, smooth transition models are assumed for the variance. We adopt the fully Bayesian approach for inference, prediction and model selection We discuss problems related to the estimation of degrees of freedom in the Student-t model and propose a solution based on independent Jeffreys priors which correct problems in the likelihood function. A simulated study is presented to investigate how the estimation of model parameters in the t-student GARCH model are affected by small sample sizes, prior distributions and misspecification regarding the sampling distribution. An application to the Dow Jones stock market data illustrates the usefulness of the asymmetric GARCH model with t-student errors.

Estimación bayesiana de un Modelo Garch-M Bivariado

“…Estas estadísticas incluyen resultados sobre la media, la asimetría y la curtosis. Cuando los datos son asimétricos y con colas pesadas, esto puede ser un indicador de que un modelo GARCH con asimetría en la volatilidad es el más apropiado [13]. Incluso, si los datos no tuvieran un coeficiente de asimetría muy alto pero la curtosis es persistente, esto sería evidencia de que un modelo GARCH con choques t-Student es el más pertinente [23].…”