This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non-parametric approaches for GARCH models that avoid imposing arbitrary pa...

This paper considers estimation of semi-nonparametric GARCH filtered copula models in which the individual time series are modeled by and joint distributions multivariate standardized innovations characterized parametric copulas with nonparametric marginal distributions. The extend those Chen Fan (2006) to allow for conditional means volatilities, estimated via method sieves. fitted residuals t...

This paper derives the statistical properties of a two-step approach to estimating multivariate rotated GARCH-BEKK (RBEKK) models. From definition RBEKK, unconditional covariance matrix is estimated in first step rotate observed variables order have identity for its sample matrix. In second step, remaining parameters are by maximizing quasi-log-likelihood function. For this quasi-maximum likeli...

This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications, the inference methods, and identifies likely directions of future research.

Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our ne...

Modeling financial volatility is an important part of empirical finance. This paper provides a literature review of the most relevant volatility models, with a particular focus on forecasting models. We firstly discuss the empirical foundations of different kinds of volatility. The paper, then, analyses the non-parametric measure of volatility, named realized variance, and its empirical applica...