Stationarity and Persistence in the GARCH(1,1) Model
给出了GARCH(1,1)过程平稳遍历的充要条件，分析了条件方差冲击的持续性，并给出了任意阶绝对矩有限的充要条件。
This paper establishes necessary and sufficient conditions for the stationarity and ergodicity of the GARCH(l.l) process. As a special case, it is shown that the IGARCH(1,1) process with no drift converges almost surely to zero, while IGARCH(1,1) with a positive drift is strictly stationary and ergodic. We examine the persistence of shocks to conditional variance in the GARCH(l.l) model, and show that whether these shocks "persist" or not depends crucially on the definition of persistence. We also develop necessary and sufficient conditions for the finiteness of absolute moments of any (including fractional) order.