It is a well-known fact that financial returns exhibit conditional heteroscedasticity and fat tails. While the GARCH-type models are very popular in depicting the conditional heteroscedasticity, the α-stable distribution is a natural candidate for the conditional distribution of financial returns. The α-stable distribution is a generalization of the normal distribution and is described by four ...

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models...

A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here...

F orecasting the volatility of a financial asset has wide implications in finance. Conditional variance extracted from the GARCH framework could be a suitable proxy of financial asset volatility. Option pricing, portfolio optimization, and risk management are examples of implications of conditional variance forecasting. One of the most recent methods of volatility forecasting is Real...

We propose a new model for volatility forecasting which combines the Generalized Dynamic Factor Model (GDFM) and the GARCH model. The GDFM, applied to a large number of series, captures the multivariate information and disentangles the common and the idiosyncratic part of each series of returns. In this financial analysis, both these components are modeled as a GARCH. We compare GDFM+GARCH and ...

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...

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...

We present a novel GARCH model that accounts for time varying, state dependent, persistence in the volatility dynamics. The proposed model generalizes the component GARCH model of Ding and Granger (1996). The volatility is modelled as a convex combination of unobserved GARCH components where the combination weights are time varying as a function of appropriately chosen state variables. In order...

GARCH models with Markov-switching regimes are often used for volatility analysis of …nancial time series. Such models imply less persistence in the conditional variance than the standard GARCH model, and potentially provide a signi…cant improvement in volatility forecast. Nevertheless, conditions for asymptotic wide-sense stationarity have been derived only for some degenerated models. In this...

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...