MCMC Bayesian Estimation in FIEGARCH Models

Bayesian inference for fractionally integrated exponential generalized autoregressive conditional heteroscedastic (FIEGARCH) models using Markov chain Monte Carlo (MCMC) methods is described. A simulation study is presented to assess the performance of the procedure, under the presence of long-memory in the volatility. Samples from FIEGARCH processes are obtained upon considering the generalized error distribution (GED) for the innovation process. Different values for the tail-thickness parameter are considered covering both scenarios, innovation processes with lighter ( > 2) and heavier ( < 2) tails than the Gaussian distribution ( = 2). A comparison between the performance of quasi-maximum likelihood (QML) and MCMC procedures is also discussed. An application of the MCMC procedure to estimate the parameters of a FIEGARCH model for the daily log-returns of the S&P500 U.S. stock market index is provided.