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Explosive volatilities for threshold-GARCH processes generated by asymmetric innovations

Authors
Hwang, S. Y.Baek, J. S.Park, J. A.Choi, M. S.
Issue Date
Jan-2010
Publisher
ELSEVIER SCIENCE BV
Citation
STATISTICS & PROBABILITY LETTERS, v.80, no.1, pp.26 - 33
Journal Title
STATISTICS & PROBABILITY LETTERS
Volume
80
Number
1
Start Page
26
End Page
33
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/13295
DOI
10.1016/j.spl.2009.09.008
ISSN
0167-7152
Abstract
The threshold-asymmetric GARCH (TGARCH, for short) models have been useful for analyzing asymmetric volatilities arising mainly from financial time series. Most of the research on TGARCH has been directed to the stationary case. In this article, motivated by unstable features in recent time series in Korea amid worldwide financial crisis, we introduce.,explosive volatilities" in TGARCH processes. The term of explosive volatility in TGARCH context is defined and is justified. Moreover, asymmetric innovations such as normal mixtures are considered in modeling explosive TGARCH and hence we are concerned with a class of explosive TGARCH models generated by asymmetric innovations. Assuming normal mixture innovations, maximum likelihood (ML) estimation method is discussed and procedures for computing ML-estimates are described. To illustrate, exchange rate data of Korea-Won to US dollars are analyzed and it is observed that the data exhibit a certain explosive volatility and in turn, our model performs better than various competing models. (C) 2009 Elsevier B.V. All rights reserved.
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