Stable GARCH models for financial time series

AbstractGeneralized autoregressive conditional heteroskedasticity (GARCH) models having normal or Student-t distributions as conditional distributions are widely used in financial modeling. Normal or Student-t distributions may be inappropriate for very heavy-tailed times series as can be encountered in financial economics, for example. Here, we propose GARCH models with stable Paretian conditional distributions to deal with such time series. We state conditions for stationarity and discuss simulation aspects