MCMC Bayesian Estimation in FIEGARCH Models

TL;DR

This paper develops a Bayesian MCMC approach for estimating FIEGARCH models, addressing long-memory volatility with various innovation tail behaviors, and analyzes the impact of prior choices and true parameter knowledge.

Contribution

It introduces a Bayesian MCMC methodology for FIEGARCH models considering different tail behaviors and prior sensitivities, which was not previously explored in detail.

Findings

MCMC effectively estimates FIEGARCH parameters with long-memory.

Tail-thickness parameter influences estimation accuracy.

Prior sensitivity impacts Bayesian inference results.

Abstract

Bayesian inference for fractionally integrated exponential generalized autoregressive conditional heteroskedastic (FIEGARCH) models using Markov Chain Monte Carlo (MCMC) methods is described. A simulation study is presented to access 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 \nu are considered covering both scenarios, innovation processes with lighter (\nu<2) and heavier (\nu>2) tails than the Gaussian distribution (\nu=2). A sensitivity analysis is performed by considering different prior density functions and by integrating (or not) the knowledge on the true parameter values to select the hyperparameter values.