Nowadays many researchers use GARCH models to generate volatility forecasts. However, it is well known that volatility persistence, as indicated by the sum of the two parameters G1 and A1[1], in GARCH models is usually too high. Since volatility forecasts in GARCH models are based on these two parameters, this may lead to poor volatility forecasts. It has long been argued that this high persist...

Since ARCH and GARCH models are presented, more and more authors are interested in the study of volatilities in financial markets with GARCH models. Method for estimating the coefficients of GARCH models is mainly the maximum likelihood estimation. Now we consider another method—MCMC method to substitute for maximum likelihood estimation method. Then we compare three GARCH models based on it. M...

We consider th e relationships between ARCH-type and stochast ic volatility models. A new class of volatility models, called generalized bilinear stochastic volatility, is described following an approach that tr ansforms an init ial GARCH-M process. Th e focus here is on th e interpretation of some simulation results, with a special care devoted to model misspecification.

This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standard...

Instantaneous dependence among several asset returns is the main reason for the computational and statistical complexities in working with full multivariate GARCH models. Using the Cholesky decomposition of the covariance matrix of such returns, we introduce a broad class of multivariate models where univariate GARCH models are used for variances of individual assets and parsimonious models for...

The autoregressive conditional heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity (GARCH) models take the dependency of the conditional second moments. The idea behind ARCH/GARCH model is quite intuitive. For ARCH models, past squared innovations describes the present squared volatility. For GARCH models, both squared innovations and the past squared volatil...

This paper proposes a new parametric volatility model that introduces serially dependent innovations in GARCH specifications. We first prove the asymptotic normality of the QML estimator in this setting, allowing for possible explosive and nonstationary behavior of the GARCH process. We show that this model can generate an alternative measure of risk premium relative to the GARCH-M. Finally, we...