The power Log-GARCH model

Exponential models of autoregressive conditional heteroscedasticity (ARCH) are attractive in empirical analysis because they guarantee the non-negativity of volatility, and because they enable richer autoregressive dynamics. However, the currently available models exhibit stability only for a limited number of conditional densities, and the available estimation and inference methods in the case where the conditional density is unknown are valid only under very restrictive assumptions. Here, we provide results and simple methods that readily enables consistent estimation and inference of univariate and multivariate power log-GARCH(P,Q) models with time-varying correlations under very general and non-restrictive assumptions, via vector ARMA(P,Q) representations. Augmented by explanatory or exogenous regressors in the volatility specification(s), our empirical applications show that the models are particularly suited for complex modelling problems where many series and/or variables are involved.