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Explosive volatilities for threshold-GARCH processes generated by asymmetric innovations

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  • Hwang, S.Y.
  • Baek, J.S.
  • Park, J.A.
  • Choi, M.S.

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.

Suggested Citation

  • Hwang, S.Y. & Baek, J.S. & Park, J.A. & Choi, M.S., 2010. "Explosive volatilities for threshold-GARCH processes generated by asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 26-33, January.
  • Handle: RePEc:eee:stapro:v:80:y:2010:i:1:p:26-33
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    2. Hwang, S. Y. & Basawa, I. V., 2004. "Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 209-220, July.
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    Cited by:

    1. Liu, Hsiang-Hsi & Chuang, Wen-I & Huang, Jih-Jeng & Chen, Yu-Hao, 2016. "The overconfident trading behavior of individual versus institutional investors," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 518-539.
    2. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
    3. Zhu, Junjun & Xie, Shiyu, 2010. "Bayesian Analysis of a Triple-Threshold GARCH Model with Application in Chinese Stock Market," MPRA Paper 28235, University Library of Munich, Germany.
    4. repec:eee:stapro:v:139:y:2018:i:c:p:20-30 is not listed on IDEAS

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