STATIONARY INTEGRATED ARCH(∞) AND AR(∞) PROCESSES WITH FINITE VARIANCE
证明了Ding和Granger关于存在有限四阶矩的平稳长记忆ARCH模型的长期猜想，并给出了协方差平稳积分AR(∞)、ARCH(∞)和FIGARCH模型存在的充要条件。
We prove the long standing conjecture of Ding and Granger (1996) about the existence of a stationary Long Memory ARCH model with finite fourth moment. This result follows from the necessary and sufficient conditions for the existence of covariance stationary integrated AR(∞), ARCH(∞), and FIGARCH models obtained in the present article. We also prove that such processes always have long memory.