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

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.

A hidden Markov regime-switching smooth transition model

In this paper, we develop a new class of parametric nonlinear time series models by combining two important classes of models, namely smooth transition models and hidden Markov regime-switching models. The class of models is general and flexible enough to incorporate two types of switching behavior: smooth state transitions and abrupt changes in hidden states. The estimation of the hidden states and model parameters is performed by applying filtering theory and a filter-based expectation-maximization (EM) algorithm. Applications of the model are illustrated using simulated data and real financial data. Other potential applications are mentioned.