Bayesian estimation of student-t garch model using lindley's approximation

Abstract

The dependency of conditional second moments of financial time series is modelled by Generalized Autoregressive conditionally heteroscedastic (GARCH) processes. The maximum likelihood estimation (MLE) procedure is most commonly used for estimating the unknown parameters of a GARCH model. In this study, the parameters of the GARCH models with student-t innovations are discussed for estimations using the Bayesian approach. It is assumed that the parameters of the GARCH model are random variables having known prior probability density functions. Lindley's approximation will be used to estimate the Bayesian estimators since they are not in a closed form. The Bayesian estimators are derived under squared error loss function. Finally, a simulation study is performed in order to compare the ML estimates to the Bayesian ones and in addition to simulations an example is given in order to illustrate the findings. MLE's and Bayesian estimates are compared according to the expected risks in the simulation study which shows that as the sample size increases the expected risks decrease and also it is observed that Bayesian estimates have performed better than MLE 's.