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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.
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 80 (2010)
    Issue (Month): 1 (January)
    Pages: 26-33

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    Handle: RePEc:eee:stapro:v:80:y:2010:i:1:p:26-33

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    References

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    1. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    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.
    3. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    4. Taewook Lee & Sangyeol Lee, 2009. "Normal Mixture Quasi-maximum Likelihood Estimator for GARCH Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 36(1), pages 157-170.
    5. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
    6. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-58, February.
    7. Hwang, S. Y. & Kim, Tae Yoon, 2004. "Power transformation and threshold modeling for ARCH innovations with applications to tests for ARCH structure," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 295-314, April.
    8. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-74, May-June.
    9. Pan, Jiazhu & Wang, Hui & Tong, Howell, 2008. "Estimation and tests for power-transformed and threshold GARCH models," Journal of Econometrics, Elsevier, vol. 142(1), pages 352-378, January.
    10. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
    11. Park, J.A. & Baek, J.S. & Hwang, S.Y., 2009. "Persistent-threshold-GARCH processes: Model and application," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 907-914, April.
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    Cited by:
    1. 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.

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