On the tail behaviors of Box-Cox transformed threshold GARCH(1,1) process

This paper considers some structural properties of Box-Cox transformed threshold GARCH(1,1) process. First, a sufficient and necessary condition for the strict stationarity of this threshold GARCH process is given. Second, some simple conditions for the existence of the moments of the threshold GARCH process are also derived. Finally, we describe the tail of the marginal distribution of the threshold GARCH process. It gives a precise meaning to the statement “light-tailed input causes heavy-tailed output”.