Método Zero-Variance para Monte Carlo Hamiltoniano aplicado a modelos GARCH univariados e multivariados

Abstract

This PhD work develops, compares and applies Monte Carlo Markov Chains (MCMC) methods for parameter estimation in univariate and multivariate GJR-GARCH models. Specifically, the following problems are addressed: (i) conception of a purely bayesian estimation approach; (ii) development of a bayesian method for higher computational efficiency in parameter estimation; and (iii) flexible selection of residual probability distributions for GJR-GARCH models. As a result from the investigations of the aforementioned problems, this work presents four contributions. The first corresponds to a bayesian inference approach for univariate and multivariate GJR-GARCH models. The second consists of studying three residual probability distributions, one of which having been inovatively employed for multivariate cases. The third combines two techniques, namely the Hamiltonian Monte Carlo (HMC) algorithm and the Zero-Variance method, to allow parameter estimation in GJR-GARCH models with higher estimator efficiency, as well as higher computational performance. Finally, the fourth presents results from simulation studies and an application over real-world data, in the context of worldwide stock market indexes, show that the proposed contributions solve the addressed problems effective and efficiently, advancing the state of the art of univariate and multivariate GARCH models.