Published online by Cambridge University Press: 17 October 2017
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.
The authors are grateful to three anonymous referees, the Co-editor, and the Editor for insightful comments, suggestions, and useful criticisms.