STATIONARY INTEGRATED ARCH(∞) AND AR(∞) PROCESSES WITH FINITE VARIANCE

Liudas Giraitis, Donatas Surgailis and Andrius Škarnulis

Econometric Theory, 2018, vol. 34, issue 6, 1159-1179

Abstract: 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.

Date: 2018
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