We present a general framework for a GARCH (1,1) type of process with innovations using a probability law of the mean-variance mixing type. We call the process the mean variance mixing GARCH (1,1) or MVM GARCH (1,1). One implication of this particular specification is a GARCH process with skewed innovations and constant mean dynamics. This is achieved without using a location parameter to compe...

a r t i c l e i n f o JEL classification: C53 G17 Keywords: GARCH Higher conditional moments Approximate predictive distributions Value-at-Risk S&P 500 Treasury bill rate Euro–US dollar exchange rate It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency...

It is well-known that the estimated GARCH dynamics exhibit common patterns. Starting from this fact we extend the Dynamic Conditional Correlation (DCC) model by allowing for a clustering structure of the univariate GARCH parameters. The model can be estimated in two steps, the first devoted to the clustering structure, and the second focusing on correlation parameters. Differently from the trad...

One of the most used methods to forecast price volatility is the generalized autoregressive conditional heteroskedasticity (GARCH) model. Nonetheless, the errors in prediction using this approach are often quite high. Hence, continued research is conducted to improve forecasting models employing a variety of techniques. In this paper, we extend the field of expert systems, forecasting, and mode...

A Skewed Student-t Realised DCC copula model using Realised Volatility GARCH marginal functions is developed within a Bayesian framework for the purpose of forecasting portfolio Value at Risk and Conditional Value at Risk. The use of copulas is implemented so that the marginal distributions can be separated from the dependence structure to produce tail forecasts. This is compared to using tradi...

GARCH-type models have been highly developed since Engle [1982] presented ARCH process 30 years ago. Different kinds of GARCH-type models are applicable to different kinds of research purposes. As documented by many literatures that short-memory processes with level shifts will exhibit properties that make standard tools conclude long-memory is present. Therefore, in this paper, we want to fore...

In financial modeling, it has been constantly pointed out that volatility clustering and conditional nonnormality induced leptokurtosis observed in high frequency data. Financial time series data are not adequately modeled by normal distribution, and empirical evidence on the non-normality assumption is well documented in the financial literature (details are illustrated by Engle (1982) and Bol...

We consider a rank-based technique for estimating GARCH model parameters, some of which are scale transformations of conventional GARCH parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given in Jaeckel (1972). They are useful for GARCH order selection and preliminary estimation. We give a limiting distribution for the rank estima...