Functional central limit theorems for ARCH(∞) models

Seunghee Choi, Oesook Lee

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In this paper, we study ARCH(∞) models with either geometrically decaying coefficients or hyperbolically decaying coefficients. Most popular autoregressive conditional heteroscedasticity (ARCH)-type models such as various modified generalized ARCH (GARCH) (p, q), fractionally integrated GARCH (FIGARCH), and hyperbolic GARCH (HYGARCH). can be expressed as one of these cases. Sufficient conditions for L2-near-epoch dependent (NED) property to hold are established and the functional central limit theorems for ARCH(∞) models are proved.

Original languageEnglish
Pages (from-to)443-455
Number of pages13
JournalCommunications for Statistical Applications and Methods
Issue number5
StatePublished - 1 Sep 2017

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the NRF funded by the Ministry of Education, Science and Technology (No. 2014R1A1A2039928 ).

Publisher Copyright:
© 2017 The Korean Statistical Society, and Korean International Statistical Society.


  • ARCH(∞) model
  • Functional central limit theorem
  • L-NED property


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