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...

A stochastic volatility model consists of a pair of stochastic processes {Xt, Yt}, of which only Yt is observed, but where the conditional distribution of Yt|Xt = xt has a scale that depends on xt. The unobserved Xt is interpreted as a state variable that affects the processes that result in the observed Yt. The conditional heteroscedasticity (CH) approach to modeling volatility is based on the...

The skewness in physical distributions of equity index returns and the implied volatility skew in the risk neutral measure are subjects of extensive academic research. Much attention is now being focused on models that are able to capture time-varying conditional skewness and kurtosis. For this reason normal mixture GARCH(1,1) models have become very popular in financial econometrics. We introd...

In this paper we introduce a multivariate generalized autoregressive conditional heteroskedastic (GARCH) class of models with time-varying eigenvalues. The dynamics the eigenvalues is derived for cases underlying Gaussian and Student’s t-distributed innovations based on general theory dynamic score by Creal, Koopman Lucas (2013) Harvey (2013). resulting eigenvalue GARCH – labeled ‘?-GARCH’ diff...

In this paper we study a new class of nonlinear GARCH models. Special interest is devoted to models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable is mainly motivated by the desire to find useful models for highly persisten...

We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter...

This paper uses a multivariate vector error-correction generalized autoregressive conditional heteroscedasticity model to investigate the effect of British grain prices on their Irish equivalents. We find that in the long run the law of one price holds and in the short run the model captures the salient features of Irish grain prices. The model is used to compute rolling forecasts of the condit...

In financial econometrics the modeling of asset return series is closely related to the estimation of the corresponding conditional densities. One reason why one is interested in the whole conditional density and not only in the conditional mean, is that the conditional variance can be interpreted as a measure of time-dependent volatility of the return series. In fact, the modeling and the pred...