The univariate Generalised Autoregressive Conditional Heterscedasticity (GARCH) model has successfully captured the symmetric conditional volatility in a wide range of time series financial returns. Although multivariate effects across assets can be captured through modelling the conditional correlations, the univariate GARCH model has two important restrictions in that it: (1) does not accommo...

We provide in this paper asymptotic theory for the multivariate GARCH(p, q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau [19] in conjunction with a result given by Boussama [9] concerning the existence of a stationary and ergodic solution to the multivariate GARCH(p, q) process. We prove asymptotic norma...

We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC method itself. It turns out that autocorrelations between the data generated with our adaptive proposal density are greatly reduced. Thus it is concluded t...

In this paper, we consider a general family of asymmetric volatility models with stationary and ergodic coefficients. This family can nest several non-linear asymmetric GARCH models with stochastic parameters into its ambit. It also generalizes Markovswitching GARCH and GJR models. The geometric ergodicity of the proposed process is established. Sufficient conditions for stationarity and existe...

We provide a closed-form estimator based on the VARMA representation for the unrestricted multivariate GARCH(1,1). We show that all parameters can be derived using basic linear algebra tools. We show that the estimator is consistent and asymptotically normal distributed. Our results allow also to derive a closed form for the parameters in the context of temporal aggregation of multivariate GARC...

In this paper the class of BL-GARCH (Bilinear General AutoregRessive Conditional Heteroskedasticity) models is introduced. The proposed model is a modification to the BL-GARCH model proposed by Storti and Vitale (2003). Stationary conditions and autocorrelation structure for special cases of these new models are derived. Maximum likelihood estimation of the model is also considered. Some simula...

This paper develops a smooth transition GARCH model with an asymmetric transition function, which allows for an asymmetric response of volatility to the size and sign of shocks, and an asymmetric transition dynamics for positive and negative shocks. We apply our model to the empirical financial data: the NASDAQ index and the individual stock IBM daily returns. The empirical evidence shows that ...

The use of GARCH models with stable Paretian innovations in financial modeling has been recently suggested in the literature. This class of processes is attractive because it allows for conditional skewness and leptokurtosis of financial returns without ruling out normality. This contribution illustrates their usefulness in predicting the downside risk of financial assets in the context of mode...

We develop a multivariate generalization of the Markov–switching GARCH model introduced by Haas, Mittnik, and Paolella (2004b) and derive its fourth– moment structure. An application to international stock markets illustrates the relevance of accounting for volatility regimes from both a statistical and economic perspective, including out–of–sample portfolio selection and computation of Value– ...