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Stationary Integrated Arch(∞) And Ar(∞) Processes With Finite Variance

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  • Giraitis, Liudas
  • Surgailis, Donatas
  • Škarnulis, Andrius

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.

Suggested Citation

  • Giraitis, Liudas & Surgailis, Donatas & Škarnulis, Andrius, 2018. "Stationary Integrated Arch(∞) And Ar(∞) Processes With Finite Variance," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1159-1179, December.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:06:p:1159-1179_00
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    Cited by:

    1. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.
    2. Royer, Julien, 2021. "Conditional asymmetry in Power ARCH($\infty$) models," MPRA Paper 109118, University Library of Munich, Germany.

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