STATIONARITY AND MEMORY OF ARCH([infty infinity]) MODELS
研究了ARCH(∞)模型（包括GARCH和长记忆模型）的协方差平稳性条件，给出了水平和平方序列平稳的充要条件，发现水平序列的平稳性排除了平方序列的长记忆性。
We establish the necessary and sufficient conditions for covariance stationarity of ARCH(∞), for both the levels and the squares. The result applies to any form of the conditional variance coefficients. This includes GARCH(p,q) and also specifications with hyperbolically decaying coefficients, such as the autoregressive coefficients of the autoregressive fractionally integrated moving average model. The covariance stationarity condition for the levels rules out long memory in the squares.I thank Peter M. Robinson for useful comments on previous versions of the paper. Also, I am grateful to the co-editor (Bruce E. Hansen) and an anonymous referee whose suggestions greatly improved the paper.