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 hold only under very specific and restrictive assumptions. Here, we provide results and simple methods that readily enables consistent estimation and inference of univariate and multivariate power log-GARCH models under very general and non-restrictive assumptions when the power is fixed, via vector ARMA representations. Additionally, stability conditions are obtained under weak assumptions, and the power log-GARCH model can be viewed as nesting certain classes of stochastic volatility models, including the common ASV(1) specification. Finally, our simulations and empirical applications suggest the model class is very useful in practice.