Stationarity and functional central limit theorem for ARCH(∞) models

Oesook Lee

doi:10.1016/j.econlet.2017.11.017

Stationarity and functional central limit theorem for ARCH(∞) models

Oesook Lee

Department of Statistics

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

Abstract

In this paper, we study the stationarity and functional central limit theorem for (random coefficient) ARCH(∞) models including HYAPGARCH and mixture memory GARCH models. Those models are able to cover long memory property with fewer parameters and have finite variances. The functional central limit theorems for u_t and the squared processes u_t ² and σ_t ² are proved. Sufficient conditions for L₂-NED property to hold are established and the FCLT for mixture memory GARCH model as an example of a random coefficient ARCH(∞) process is derived via L₂-NED condition.

Original language	English
Pages (from-to)	107-111
Number of pages	5
Journal	Economics Letters
Volume	162
DOIs	https://doi.org/10.1016/j.econlet.2017.11.017
State	Published - Jan 2018

Bibliographical note

Funding Information:
I am grateful to the Editor and an anonymous referee for their helpful comments. This research was supported by Basic Science Research Program through the NRF funded by the Ministry of Education, Science and Technology ( 2014R1A1A2039928 ).

Publisher Copyright:
© 2017

Keywords

Functional central limit theorem
L-NED property
Mixture memory GARCH process
Random coefficient ARCH(∞) process

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10.1016/j.econlet.2017.11.017

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abstract = "In this paper, we study the stationarity and functional central limit theorem for (random coefficient) ARCH(∞) models including HYAPGARCH and mixture memory GARCH models. Those models are able to cover long memory property with fewer parameters and have finite variances. The functional central limit theorems for ut and the squared processes ut 2 and σt 2 are proved. Sufficient conditions for L2-NED property to hold are established and the FCLT for mixture memory GARCH model as an example of a random coefficient ARCH(∞) process is derived via L2-NED condition.",

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N2 - In this paper, we study the stationarity and functional central limit theorem for (random coefficient) ARCH(∞) models including HYAPGARCH and mixture memory GARCH models. Those models are able to cover long memory property with fewer parameters and have finite variances. The functional central limit theorems for ut and the squared processes ut 2 and σt 2 are proved. Sufficient conditions for L2-NED property to hold are established and the FCLT for mixture memory GARCH model as an example of a random coefficient ARCH(∞) process is derived via L2-NED condition.

AB - In this paper, we study the stationarity and functional central limit theorem for (random coefficient) ARCH(∞) models including HYAPGARCH and mixture memory GARCH models. Those models are able to cover long memory property with fewer parameters and have finite variances. The functional central limit theorems for ut and the squared processes ut 2 and σt 2 are proved. Sufficient conditions for L2-NED property to hold are established and the FCLT for mixture memory GARCH model as an example of a random coefficient ARCH(∞) process is derived via L2-NED condition.

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JO - Economics Letters

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Stationarity and functional central limit theorem for ARCH(∞) models

Abstract

Bibliographical note

Keywords

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