Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Cumulative Impulse Response Functions for a Class of Threshold-Asymmetric GARCH Processes

  • Park, J.A. (Department of Statistics, Sookmyung Women's University) ;
  • Baek, J.S. (Department of Statistics, Sookmyung Women's University) ;
  • Hwang, S.Y. (Department of Statistics, Sookmyung Women's University)
  • Received : 20100200
  • Accepted : 20100200
  • Published : 2010.03.31
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Abstract

A class of threshold-asymmetric GRACH(TGARCH, hereafter) models has been useful for explaining asymmetric volatilities in the field of financial time series. The cumulative impulse response function of a conditionally heteroscedastic time series often measures a degree of unstability in volatilities. In this article, a general form of the cumulative impulse response function of the TGARCH model is discussed. In particular, We present formula in their closed forms for the first two lower order models, viz., TGARCH(1, 1) and TGARCH(2, 2).

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References

  1. Baillie, R. T., Bollerslev, T. and Mikkelsen, H. O. (1996). Fractionally integrated generalized autore-gressive conditional heteroskedasticity, Journal of Econometrics, 74, 3-30. https://doi.org/10.1016/S0304-4076(95)01749-6
  2. Blockewell. P. J. and Davis, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer-Verlag, New York.
  3. Bollerslev, T. (1986). Generalized autoegressive conditional heteroscedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  4. Conrad, C. and Karanasos, M. (2006). The impulse response function of the long memory GARCH process, Economics Letters, 90, 34-41. https://doi.org/10.1016/j.econlet.2005.07.001
  5. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1008. https://doi.org/10.2307/1912773
  6. Hwang, S. W. and Basawa, I. V. (2004). Stationarity and moment structure for Box-Cox transformed threshold GARCH(1, 1) processes, Statistics & Probability Letters, 68, 209-220. https://doi.org/10.1016/j.spl.2003.08.016
  7. Hwang, S. Y., Baek, J. S., Park, J. A. and Choi, M. S. (2010). Explosive volatilities for the threshold GARCH processes generated by asymmetric innovations, Statistics & Probability Letters, 80, 26-33. https://doi.org/10.1016/j.spl.2009.09.008
  8. Li, C. W. and Li, W. K. (1996). On an double-threshold autoregressive heteroscedastic time series model, Journal of Applied Econometrics, 11, 253-274. https://doi.org/10.1002/(SICI)1099-1255(199605)11:3<253::AID-JAE393>3.0.CO;2-8
  9. Liu, J. C. (2006). On the tail behaviors of Box-Cox transformed threshold GARCH(1, 1) process, Statistics & Probability Letters, 76, 1323-1330. https://doi.org/10.1016/j.spl.2006.01.009
  10. Pan, J. Z., Wang, H. and Tong, H. (2008). Estimation and tests for power-transformed and threshold GARCH models, Journal of Econometrics, 142, 352-378. https://doi.org/10.1016/j.jeconom.2007.06.004
  11. Park, J. A., Baek, J. S. ,and Hwang, S. Y. (2009). Persistent threshold-GARCH processes: Model and application, Statistics & Probability Letters, 79, 907-914. https://doi.org/10.1016/j.spl.2008.11.018
  12. Rabemananjara, R. and Zakoian, J. M. (1993). Threshold ARCH models and asymmetries in volatility, Journal of Applied Econometrics, 8, 31-49. https://doi.org/10.1002/jae.3950080104