Functional central limit theorems for ARCH(∞) models

Seunghee Choi; Oesook Lee

doi:10.5351/CSAM.2017.24.5.443

Functional central limit theorems for ARCH(∞) models

Seunghee Choi, Oesook Lee

Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 language	English
Pages (from-to)	443-455
Number of pages	13
Journal	Communications for Statistical Applications and Methods
Volume	24
Issue number	5
DOIs	https://doi.org/10.5351/CSAM.2017.24.5.443
State	Published - 1 Sep 2017

Keywords

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

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10.5351/CSAM.2017.24.5.443

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title = "Functional central limit theorems for ARCH(∞) models",

abstract = "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.",

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N2 - 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.

AB - 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.

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Functional central limit theorems for ARCH(∞) models

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Keywords

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