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  • Liudas Giraitis (a1), Donatas Surgailis (a2) and Andrius Škarnulis (a2)

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.

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*Address correspondence to Liudas Giraitis, School of Economics and Finance, QMUL, Mile End Road, London E1 4NS, UK; e-mail:
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The authors are grateful to three anonymous referees, the Co-editor, and the Editor for insightful comments, suggestions, and useful criticisms.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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