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.

This article investigates what type of nominal price rigidity there is in Brazil by testing if there are different price responses to sector-specific, monetary policy, and exchange rate shocks. We estimate the effects of these shocks on disaggregated prices of the Brazilian consumer price index (IPCA), from 1999 to 2011, using a factor-augmented vector autoregressive model (FAVAR). There is innovation in the Bayesian technique used to estimate the model, which allows for the consistent imposition of priors directly on the parameters of the structural form of the model and the use of sign restrictions in the impulse responses to identify the model. We combine the Gibbs sampling procedure developed by Bernanke, Boivin, and Eliasz (2004) to estimate a FAVAR with the Gibbs sampling procedure developed by Waggoner and Zha (2002 and 2007) to estimate a Bayesian structural vector autoregressive model (BSVAR). The main results are: (i) series-specific shocks are the main determinants of variances in highly disaggregated price series, but macroeconomic shocks have more influence over aggregated series; (ii) macroeconomic shocks are more persistent than series-specific shocks; (iii) almost all the signs of the price responses to monetary and exchange rate shocks are the ones predicted by the theory; and (iv) the magnitude of the responses to monetary and exchange rate shocks are heterogeneous across sectors.